Radiomic Quantification for MRI Assessment of Sacroiliac Joints of Patients with Spondyloarthritis

Spondyloarthritis (SpA) is a group of diseases primarily involving chronic inflammation of the spine and peripheral joints, as evaluated by magnetic resonance imaging (MRI). Considering the complexity of SpA, we performed a retrospective study to discover quantitative/radiomic MRI-based features correlated with SpA. We also investigated different fat-suppression MRI techniques to develop detection models for inflammatory sacroiliitis. Finally, these model results were compared with those of experienced musculoskeletal radiologists, and the concordance level was evaluated. Examinations of 46 consecutive patients were obtained using SPAIR (spectral attenuated inversion recovery) and STIR (short tau inversion recovery) MRI sequences. Musculoskeletal radiologists manually segmented the sacroiliac joints for further extraction of 230 MRI features from gray-level histogram/matrices and wavelet filters. These features were associated with sacroiliitis, SpA, and the current biomarkers of ESR (erythrocyte sedimentation rate), CRP (C-reactive protein), BASDAI (Bath Ankylosing Spondylitis Activity Index), BASFI (Bath Ankylosing Spondylitis Functional Index), and MASES (Maastricht Ankylosing Spondylitis Enthesis Score). The Mann-Whitney U test showed that the radiomic markers from both MRI sequences were associated with active sacroiliitis and with SpA and its axial and peripheral subtypes (p < 0.05). Spearman's coefficient also identified a correlation between MRI markers and data from clinical practice (p < 0.05). Fat-suppression MRI models yielded performances that were statistically equivalent to those of specialists and presented strong concordance in identifying inflammatory sacroiliitis. SPAIR and STIR acquisition protocols showed potential for the evaluation of sacroiliac joints and the composition of a radiomic model to support the clinical assessment of SpA.

Machine learning techniques for computer-aided classification of active inflammatory sacroiliitis in magnetic resonance imaging

Background

Currently, magnetic resonance imaging (MRI) is used to evaluate active inflammatory sacroiliitis related to axial spondyloarthritis (axSpA). The qualitative and semiquantitative diagnosis performed by expert radiologists and rheumatologists remains subject to significant intrapersonal and interpersonal variation. This encouraged us to use machine-learning methods for this task.

Methods

In this retrospective study including 56 sacroiliac joint MRI exams, 24 patients had positive and 32 had negative findings for inflammatory sacroiliitis according to the ASAS group criteria. The dataset was randomly split with ~ 80% (46 samples, 20 positive and 26 negative) as training and ~ 20% as external test (10 samples, 4 positive and 6 negative). After manual segmentation of the images by a musculoskeletal radiologist, multiple features were extracted. The classifiers used were the Support Vector Machine, the Multilayer Perceptron (MLP), and the Instance-Based Algorithm, combined with the Relief and Wrapper methods for feature selection.

Results

Based on 10-fold cross-validation using the training dataset, the MLP classifier obtained the best performance with sensitivity = 100%, specificity = 95.6% and accuracy = 84.7%, using 6 features selected by the Wrapper method. Using the test dataset (external validation) the same MLP classifier obtained sensitivity = 100%, specificity = 66.7% and accuracy = 80%.

Conclusions

Our results show the potential of machine learning methods to identify SIJ subchondral bone marrow edema in axSpA patients and are promising to aid in the detection of active inflammatory sacroiliitis on MRI STIR sequences. Multilayer Perceptron (MLP) achieved the best results.

Manual and semiautomatic segmentation of bone sarcomas on MRI have high similarity

The aims of this study were to evaluate the intra- and interobserver reproducibility of manual segmentation of bone sarcomas in magnetic resonance imaging (MRI) studies and to compare manual and semiautomatic segmentation methods. This retrospective study included twelve osteosarcoma and eight Ewing sarcoma MRI studies performed prior to any therapeutic intervention. All cases were histopathologically confirmed. Three radiologists used 3D-Slicer software to perform manual segmentation of bone sarcomas in a blinded and independent manner. One radiologist segmented manually and also performed semiautomatic segmentation with the GrowCut tool. Segmentation exercises were timed for comparison. The dice similarity coefficient (DSC) and Hausdorff distance (HD) were used to evaluate similarity between the segmentation results and further statistical analyses were performed to compare DSC, HD, and volumetric results. Manual segmentation was reproducible with intraobserver DSC varying from 0.83 to 0.97 and HD from 3.37 to 28.73 mm. Interobserver DSC of manual segmentation showed variation from 0.73 to 0.97 and HD from 3.93 to 33.40 mm. Semiautomatic segmentation compared to manual segmentation resulted in DSCs of 0.71−0.96 and HDs of 5.38−31.54 mm. Semiautomatic segmentation required significantly less time compared to manual segmentation (P value ≤0.05). Among all situations compared, tumor volumetry did not show significant statistical differences (P value >0.05). We found excellent intra- and interobserver agreement for manual segmentation of osteosarcoma and Ewing sarcoma. There was high similarity between manual and semiautomatic segmentation, with a significant reduction of segmentation time using the semiautomatic method.

Shape, texture and statistical features for classification of benign and malignant vertebral compression fractures in magnetic resonance images

PURPOSE

Vertebral compression fractures (VCFs) result in partial collapse of vertebral bodies. They usually are nontraumatic or occur with low-energy trauma in the elderly secondary to different etiologies, such as insufficiency fractures of bone fragility in osteoporosis (benign fractures) or vertebral metastasis (malignant fractures). Our study aims to classify VCFs in T1-weighted magnetic resonance images (MRI).

METHODS

We used the median sagittal planes of lumbar spine MRIs from 63 patients (38 women and 25 men) previously diagnosed with VCFs. The lumbar vertebral bodies were manually segmented and statistical features of gray levels were computed from the histogram. We also extracted texture and shape features to analyze the contours of the vertebral bodies. In total, 102 lumbar VCFs (53 benign and 49 malignant) and 89 normal lumbar vertebral bodies were analyzed. The k-nearest-neighbor method, a neural network with radial basis functions, and a naïve Bayes classifier were used with feature selection. We compared the classification obtained by these classifiers with the final diagnosis of each case, including biopsy for the malignant fractures and clinical and laboratory follow up for the benign fractures.

RESULTS

The results obtained show an area under the receiver operating characteristic curve of 0.97 in distinguishing between normal and fractured vertebral bodies, and 0.92 in discriminating between benign and malignant fractures.

CONCLUSIONS

The proposed classification methods based on shape, texture, and statistical features have provided high accuracy and may assist in the diagnosis of VCFs.

Classification of vertebral compression fractures in magnetic resonance images using spectral and fractal analysis

Fractures with partial collapse of vertebral bodies are generically referred to as "vertebral compression fractures" or VCFs. VCFs can have different etiologies comprising trauma, bone failure related to osteoporosis, or metastatic cancer affecting bone. VCFs related to osteoporosis (benign fractures) and to cancer (malignant fractures) are commonly found in the elderly population. In the clinical setting, the differentiation between benign and malignant fractures is complex and difficult. This paper presents a study aimed at developing a system for computer-aided diagnosis to help in the differentiation between malignant and benign VCFs in magnetic resonance imaging (MRI). We used T1-weighted MRI of the lumbar spine in the sagittal plane. Images from 47 consecutive patients (31 women, 16 men, mean age 63 years) were studied, including 19 malignant fractures and 54 benign fractures. Spectral and fractal features were extracted from manually segmented images of 73 vertebral bodies with VCFs. The classification of malignant vs. benign VCFs was performed using the k-nearest neighbor classifier with the Euclidean distance. Results obtained show that combinations of features derived from Fourier and wavelet transforms, together with the fractal dimension, were able to obtain correct classification rate up to 94.7% with area under the receiver operating characteristic curve up to 0.95.

Automatic detection of the nipple in screen-film and full-field digital mammograms using a novel Hessian-based method

Automatic detection of the nipple in mammograms is an important step in computerized systems that combine multiview information for accurate detection and diagnosis of breast cancer. Locating the nipple is a difficult task owing to variations in image quality, presence of noise, and distortion and displacement of the breast tissue due to compression. In this work, we propose a novel Hessian-based method to locate automatically the nipple in screen-film and full-field digital mammograms (FFDMs). The method includes detection of a plausible nipple/retroareolar area in a mammogram using geometrical constraints, analysis of the gradient vector field by mean and Gaussian curvature measurements, and local shape-based conditions. The proposed procedure was tested on 566 mammographic images consisting of 372 randomly selected scanned films from two public databases (mini-MIAS and DDSM), and 194 digital mammograms acquired with a GE Senographe 2000D FFDM system. A radiologist independently marked the centers of the nipples for evaluation of the results. The average error obtained was 6.7 mm (22 pixels) with reference to the center of the nipple as identified by the radiologist. Only two out of the 566 detected nipples (0.35 %) had an error larger than 50 mm. The method was also directly compared with two other techniques for the detection of the nipple. The results indicate that the proposed method outperforms other algorithms presented in the literature and can be used to identify accurately the nipple on various types of mammographic images.

Analysis of knee joint sound signals for non-invasive diagnosis of cartilage pathology

The need for a safe, objective, noninvasive tool for the early detection, localization, and quantification of both hyaline articular cartilage and meniscal pathology in the knee is discussed, and the possible use of joint sounds for this purpose is examined. A historical survey of joint sound analysis is given, and the authors' own research is described. The analysis of the knee joint sounds, using time-domain signal plots and three-dimensional spectral plots, supported the authors' assumptions regarding the nature of various degrees of chondromalacia and meniscal lesions, and the associated sounds. Quantitative features such as energy, frequency peaks, duration of signal components, and bandwidths can be easily computed from the data. Further subclassification, however, would require more accurate quantification or parametric representation of signal features, which should be possible by modeling techniques such as linear prediction.

The application of Efron's bootstrap methods in validating feature classification using artificial neural networks for the analysis of mammographic masses

Efron's bootstrap resampling method is used to analyze the performance of artificial neural networks (ANNs) in the area of feature classification for the analysis of mammographic masses. The purpose of feature classification in mammography is to discover the salient information that can be used to discriminate benign from malignant masses. The performance of ANNs is typically measured in terms of the area under the receiver operating characteristics (ROC) curve (A/sub z/). Performance uncertainty problems and the generalization problems of ANNs are still the critical issues that impede the further application of ANNs in clinical medicine. It is unreasonable and impractical to justify the performance of one ANN being better than another just by its best A/sub z/ value. Efron's bootstrap methods make it possible to quantitatively analyze the performance of ANNs and anticipate its change tendency with relatively high accuracy. Our experimental results show that the probability model of A/sub z/ is close to a normal distribution. The performance of ANNs is more sensitive to the change of topology than that of the size and the composition of the training set. Bootstrap methods can be used to find the optimal epochs and avoid overfitting.

Content-based retrieval of mammograms using visual features related to breast density patterns

This paper describes part of content-based image retrieval (CBIR) system that has been developed for mammograms. Details are presented of methods implemented to derive measures of similarity based upon structural characteristics and distributions of density of the fibroglandular tissue, as well as the anatomical size and shape of the breast region as seen on the mammogram. Well-known features related to shape, size, and texture (statistics of the gray-level histogram, Haralick's texture features, and moment-based features) were applied, as well as less-explored features based in the Radon domain and granulometric measures. The Kohonen self-organizing map (SOM) neural network was used to perform the retrieval operation. Performance evaluation was done using precision and recall curves obtained from comparison between the query and retrieved images. The proposed methodology was tested with 1,080 mammograms, including craniocaudal and mediolateral-oblique views. Precision rates obtained are in the range from 79% to 83% considering the total image set. Considering the first 50% of the retrieved mages, the precision rates are in the range from 78% to 83%; the rates are in the range from 79% to 86% considering the first 25% of the retrieved images. Results obtained indicate the potential of the implemented methodology to serve as a part of a CBIR system for mammography.

Classification of breast masses in mammograms using genetic programming and feature selection

Mammography is a widely used screening tool and is the gold standard for the early detection of breast cancer. The classification of breast masses into the benign and malignant categories is an important problem in the area of computer-aided diagnosis of breast cancer. A small dataset of 57 breast mass images, each with 22 features computed, was used in this investigation; the same dataset has been previously used in other studies. The extracted features relate to edge-sharpness, shape, and texture. The novelty of this paper is the adaptation and application of the classification technique called genetic programming (GP), which possesses feature selection implicitly. To refine the pool of features available to the GP classifier, we used feature-selection methods, including the introduction of three statistical measures--Student's t test, Kolmogorov-Smirnov test, and Kullback-Leibler divergence. Both the training and test accuracies obtained were high: above 99.5% for training and typically above 98% for test experiments. A leave-one-out experiment showed 97.3% success in the classification of benign masses and 95.0% success in the classification of malignant tumors. A shape feature known as fractional concavity was found to be the most important among those tested, since it was automatically selected by the GP classifier in almost every experiment.

Segmentation of the fibro-glandular disc in mammograms using Gaussian mixture modelling

The paper presents a technique for the segmentation of the fibro-glandular disc in mammograms based upon a statistical model of breast density. The density function of the model was represented by a mixture of up to four weighted Gaussians, each one corresponding to a specific density class in the breast. The parameters of the model and the number of tissue classes in the breast were determined using the expectation-maximisation algorithm and the minimum description length method. Grey-level statistics of the pectoral muscle were used to determine the tissue categories that are likely to represent the fibro-glandular disc. The method was applied to 84 medio-lateral oblique mammograms from the Mini-MIAS database. The results of the segmented fibro-glandular disc were assessed by a radiologist using the original and the segmented images, with reference to a ranking table categorising the results of segmentation as: 1: excellent; 2: good; 3: average; 4: poor; and 5: complete failure. Of the 84 cases analysed, 64.3% were rated as excellent, 16.7% were rated as good, 10.7% were rated as average, and 4.7% were rated as poor; only 3.6% of the cases were rated as a complete failure with regard to segmentation of the fibro-glandular disc.

Estimation of the tissue composition of the tumour mass in neuroblastoma using segmented CT images

Neuroblastoma is the most common extra-cranial, solid, malignant tumour in children. Advances in radiology have made possible the detection and staging of the disease. Nevertheless, there is no method available at present that can go beyond detection and qualitative analysis, towards quantitative assessment of the tissue composition of the primary tumour mass in neuroblastoma. Such quantitative analysis could provide important information and serve as a decision-support tool to the radiologist and the oncologist, result in better treatment and follow-up and even lead to the avoidance of delayed surgery. The problem investigated was the improvement of the analysis of the primary tumour mass, in patients with neuroblastoma, using X-ray computed tomography (CT) images. A methodology was proposed for the estimation of the tissue content of the mass: it comprised a Gaussian mixture model for estimation, from segmented CT images, of the tissue composition of the primary tumour. To demonstrate the potential of the method, the results are presented of its application to ten CT examinations of four patients. The method provides quantitative information, and it was observed that the tumour in one of the patients reduced from 523 cm3 to 81 cm3 in volume, with an increase in calcification from about 20% to about 88% of the tumour volume, in response to chemotherapy over a period of five months. Results indicate that the proposed technique may be of considerable value in assessing the response to therapy of patients with neuroblastoma.

Identification of the breast boundary in mammograms using active contour models

A method for the identification of the breast boundary in mammograms is presented. The method can be used in the preprocessing stage of a system for computer-aided diagnosis (CAD) of breast cancer and also in the reduction of image file size in picture archiving and communication system applications. The method started with modification of the contrast of the original image. A binarisation procedure was then applied to the image, and the chain-code algorithm was used to find an approximate breast contour. Finally, the identification of the true breast boundary was performed by using the approximate contour as the input to an active contour model algorithm specially tailored for this purpose. After demarcation of the breast boundary, all artifacts outside the breast region were eliminated. The method was applied to 84 medio-lateral oblique mammograms from the Mini-MIAS database. Evaluation of the detected breast boundary was performed based upon the percentage of false-positive and false-negative pixels determined by a quantitative comparison between the contours identified by a radiologist and those identified by the proposed method. The average false positive and false negative rates were 0.41% and 0.58%, respectively. The two radiologists who evaluated the results considered the segmentation results to be acceptable for CAD purposes.

Automatic identification of the pectoral muscle in mammograms

The pectoral muscle represents a predominant density region in most medio-lateral oblique (MLO) views of mammograms; its inclusion can affect the results of intensity-based image processing methods or bias procedures in the detection of breast cancer. Local analysis of the pectoral muscle may be used to identify the presence of abnormal axillary lymph nodes, which may be the only manifestation of occult breast carcinoma. We propose a new method for the identification of the pectoral muscle in MLO mammograms based upon a multiresolution technique using Gabor wavelets. This new method overcomes the limitation of the straight-line representation considered in our initial investigation using the Hough transform. The method starts by convolving a group of Gabor filters, specially designed for enhancing the pectoral muscle edge, with the region of interest containing the pectoral muscle. After computing the magnitude and phase images using a vector-summation procedure, the magnitude value of each pixel is propagated in the direction of the phase. The resulting image is then used to detect the relevant edges. Finally, a post-processing stage is used to find the true pectoral muscle edge. The method was applied to 84 MLO mammograms from the Mini-MIAS (Mammographic Image Analysis Society, London, U.K.) database. Evaluation of the pectoral muscle edge detected in the mammograms was performed based upon the percentage of false-positive (FP) and false-negative (FN) pixels determined by comparison between the numbers of pixels enclosed in the regions delimited by the edges identified by a radiologist and by the proposed method. The average FP and FN rates were, respectively, 0.58% and 5.77%. Furthermore, the results of the Gabor-filter-based method indicated low Hausdorff distances with respect to the hand-drawn pectoral muscle edges, with the mean and standard deviation being 3.84 +/- 1.73 mm over 84 images.

Auditory display of knee-joint vibration signals

Sounds generated due to rubbing of knee-joint surfaces may lead to a potential tool for noninvasive assessment of articular cartilage degeneration. In the work reported in the present paper, an attempt is made to perform computer-assisted auscultation of knee joints by auditory display (AD) of vibration signals (also known as vibroarthrographic or VAG signals) emitted during active movement of the leg. Two types of AD methods are considered: audification and sonification. In audification, the VAG signals are scaled in time and frequency using a time-frequency distribution to facilitate aural analysis. In sonification, the instantaneous mean frequency and envelope of the VAG signals are derived and used to synthesize sounds that are expected to facilitate more accurate diagnosis than the original signals by improving their aural quality. Auditory classification experiments were performed by two orthopedic surgeons with 37 VAG signals including 19 normal and 18 abnormal cases. Sensitivity values (correct detection of abnormality) of 31%, 44%, and 83%, and overall classification accuracies of 53%, 40%, and 57% were obtained with the direct playback, audification, and sonification methods, respectively. The corresponding d' scores were estimated to be 1.10. -0.36, and 0.55. The high sensitivity of the sonification method indicates that the technique could lead to improved detection of knee-joint abnormalities; however, additional work is required to improve its specificity and achieve better overall performance.

Detection of breast masses in mammograms by density slicing and texture flow-field analysis

We propose a method for the detection of masses in mammographic images that employs Gaussian smoothing and sub-sampling operations as preprocessing steps. The mass portions are segmented by establishing intensity links from the central portions of masses into the surrounding areas. We introduce methods for analyzing oriented flow-like textural information in mammograms. Features based on flow orientation in adaptive ribbons of pixels across the margins of masses are proposed to classify the regions detected as true mass regions or false-positives (FPs). The methods yielded a mass versus normal tissue classification accuracy represented as an area (Az) of 0.87 under the receiver operating characteristics (ROCs) curve with a dataset of 56 images including 30 benign disease, 13 malignant disease, and 13 normal cases selected from the mini Mammographic Image Analysis Society database. A sensitivity of 81% was achieved at 2.2 FPs/image. Malignant tumor versus normal tissue classification resulted in a higher Az value of 0.9 under the ROC curve using only the 13 malignant and 13 normal cases with a sensitivity of 85% at 2.45 FPs/image. The mass detection algorithm could detect all the 13 malignant tumors successfully, but achieved a success rate of only 63% (19/30) in detecting the benign masses. The mass regions that were successfully segmented were further classified as benign or malignant disease by computing five texture features based on gray-level co-occurrence matrices (GCMs) and using the features in a logistic regression method. The features were computed using adaptive ribbons of pixels across the boundaries of the masses. Benign versus malignant classification using the GCM-based texture features resulted in Az = 0.79 with 19 benign and 13 malignant cases.

Analysis of asymmetry in mammograms via directional filtering with Gabor wavelets

This paper presents a procedure for the analysis of left-right (bilateral) asymmetry in mammograms. The procedure is based upon the detection of linear directional components by using a multiresolution representation based upon Gabor wavelets. A particular wavelet scheme with two-dimensional Gabor filters as elementary functions with varying tuning frequency and orientation, specifically designed in order to reduce the redundancy in the wavelet-based representation, is applied to the given image. The filter responses for different scales and orientation are analyzed by using the Karhunen-Loève (KL) transform and Otsu's method of thresholding. The KL transform is applied to select the principal components of the filter responses, preserving only the most relevant directional elements appearing at all scales. The selected principal components, thresholded by using Otsu's method, are used to obtain the magnitude and phase of the directional components of the image. Rose diagrams computed from the phase images and statistical measures computed thereof are used for quantitative and qualitative analysis of the oriented patterns. A total of 80 images from 20 normal cases, 14 asymmetric cases, and six architectural distortion cases from the Mini-MIAS (Mammographic Image Analysis Society, London, U.K.) database were used to evaluate the scheme using the leave-one-out methodology. Average classification accuracy rates of up to 74.4% were achieved.

Gradient and texture analysis for the classification of mammographic masses

Computer-aided classification of benign and malignant masses on mammograms is attempted in this study by computing gradient-based and texture-based features. Features computed based on gray-level co-occurrence matrices (GCMs) are used to evaluate the effectiveness of textural information possessed by mass regions in comparison with the textural information present in mass margins. A method involving polygonal modeling of boundaries is proposed for the extraction of a ribbon of pixels across mass margins. Two gradient-based features are developed to estimate the sharpness of mass boundaries in the ribbons of pixels extracted from their margins. A total of 54 images (28 benign and 26 malignant) containing 39 images from the Mammographic Image Analysis Society (MIAS) database and 15 images from a local database are analyzed. The best benign versus malignant classification of 82.1%, with an area (Az) of 0.85 under the receiver operating characteristics (ROC) curve, was obtained with the images from the MIAS database by using GCM-based texture features computed from mass margins. The classification method used is based on posterior probabilities computed from Mahalanobis distances. The corresponding accuracy using jack-knife classification was observed to be 74.4%, with Az = 0.67. Gradient-based features achieved Az = 0.6 on the MIAS database and Az = 0.76 on the combined database. The corresponding values obtained using jack-knife classification were observed to be 0.52 and 0.73 for the MIAS and combined databases, respectively.

Boundary modelling and shape analysis methods for classification of mammographic masses

The problem of computer-aided classification of benign and malignant breast masses using shape features is addressed. The aim of the study is to look at the exceptions in shapes of masses such as circumscribed malignant tumours and spiculated benign masses which are difficult to classify correctly using common shape analysis methods. The proposed methods of shape analysis treat the object's boundary in terms of local details. The boundaries of masses analysed using the proposed methods were manually drawn on mammographic images by an expert radiologist (JELD). A boundary segmentation method is used to separate major portions of the boundary and to label them as concave or convex segments. To analyse the shape information localised in each segment, features are computed through an iterative procedure for polygonal modelling of the mass boundaries. Features are based on the concavity fraction of a mass boundary and the degree of narrowness of spicules as characterised by a spiculation index. Two features comprising spiculation index (SI) and fractional concavity (fcc) developed in the present study when used in combination with the global shape feature of compactness resulted in a benign/malignant classification accuracy of 82%, with an area (Az) of 0.79 under the receiver operating characteristics (ROC) curve with a database of the boundaries of 28 benign masses and 26 malignant tumours. SI alone resulted in a classification accuracy of 80% with Az of 0.82. The combination of all the three features achieved 91% accuracy of circumscribed versus spiculated classification of masses based on shape.

Adaptive time-frequency analysis of knee joint vibroarthrographic signals for noninvasive screening of articular cartilage pathology

Vibroarthrographic (VAG) signals emitted by human knee joints are nonstationary and multicomponent in nature; time-frequency distributions (TFD's) provide powerful means to analyze such signals. The objective of this paper is to construct adaptive TFD's of VAG signals suitable for feature extraction. An adaptive TFD was constructed by minimum cross-entropy optimization of the TFD obtained by the matching pursuit decomposition algorithm. Parameters of VAG signals such as energy, energy spread, frequency, and frequency spread were extracted from their adaptive TFD's. The parameters carry information about the combined TF dynamics of the signals. The mean and standard deviation of the parameters were computed, and each VAG signal was represented by a set of just six features. Statistical pattern classification experiments based on logistic regression analysis of the parameters showed an overall normal/abnormal screening accuracy of 68.9% with 90 VAG signals (51 normals and 39 abnormals), and a higher accuracy of 77.5% with a database of 71 signals with 51 normals and 20 abnormals of a specific type of patellofemoral disorder. The proposed method of VAG signal analysis is independent of joint angle and clinical information, and shows good potential for noninvasive diagnosis and monitoring of patellofemoral disorders such as chondromalacia patella.

Automatic de-noising of knee-joint vibration signals using adaptive time-frequency representations

A novel de-noising method for improving the signal-to-noise ratio of knee-joint vibration signals (also known as vibro-arthrographic (VAG) signals) is proposed. The de-noising methods considered are based on signal decomposition techniques, such as wavelets, wavelet packets and the matching pursuit (MP) method. Performance evaluation with synthetic signals simulated with the characteristics expected of VAG signals indicates good de-noising results with the MP method. Statistical pattern classification of non-stationary signal features extracted from time-frequency distributions of 37 (19 normal and 18 abnormal) MP method-de-noised VAG signals shows a sensitivity of 83.3%, a specificity of 84.2% and an overall accuracy of 83.8%.

Adaptive-neighborhood filtering of images corrupted by signal-dependent noise

In many image-processing applications the noise that corrupts the images is signal dependent, the most widely encountered types being multiplicative, Poisson, film-grain, and speckle noise. Their common feature is that the power of the noise is related to the brightness of the corrupted pixel. This results in brighter areas appearing to be noisier than darker areas. We propose a new adaptive-neighborhood approach to filtering images corrupted by signal-dependent noise. Instead of using fixed-size, fixed-shape neighborhoods, statistics of the noise and the signal are computed within variable-size, variable-shape neighborhoods that are grown for every pixel to contain only pixels that belong to the same object. Results of adaptive-neighborhood filtering are compared with those given by two local-statistics-based filters (the refined Lee filter and the noise-updating repeated Wiener filter), both in terms of subjective and objective measures. The adaptive-neighborhood approach provides better noise suppression as indicated by lower mean-squared errors as well as better retention of edge sharpness than the other approaches considered.

Measures of acutance and shape for classification of breast tumors

Most benign breast tumors possess well-defined, sharp boundaries that delineate them from surrounding tissues, as opposed to malignant tumors. Computer techniques proposed to date for tumor analysis have concentrated on shape factors of tumor regions and texture measures. While shape measures based on contours of tumor regions can indicate differences in shape complexities between circumscribed and spiculated tumors, they are not designed to characterize the density variations across the boundary of a tumor. In this paper we propose a region-based measure of image edge profile acutance which characterizes the transition in density of a region of interest (ROI) along normals to the ROI at every boundary pixel. We investigate the potential of acutance in quantifying the sharpness of the boundaries of tumors, and propose its application to discriminate between benign and malignant mammographic tumors. In addition, we study the complementary use of various shape factors based upon the shape of the ROI, such as compactness, Fourier descriptors, moments, and chord-length statistics to distinguish between circumscribed and spiculated tumors. Thirty-nine images from the Mammographic Image Analysis Society (MIAS) database and an additional set of 15 local cases were selected for this study. The cases included 16 circumscribed benign, seven circumscribed malignant, 12 spiculated benign, and 19 spiculated malignant lesions. All diagnoses were proven by pathologic examinations of resected tissue. The contours of the lesions were first marked by an expert radiologist using X-Paint and X-Windows on a SUN-SPARCstation 2 Workstation. For computation of acutance, the ROI boundaries were iteratively approximated using a split/merge and end-point adjustment technique to obtain the best-fitting polygonal approximation. The jackknife method using the Mahalanobis distance measure in the BMDP (Biomedical Programs) package was used for classification of the lesions using acutance and the shape factors as features in various combinations. Acutance alone resulted in a benign/malignant classification accuracy of 95% the MIAS cases. Compactness alone gave a circumscribed/spiculated classification rate of 92.3% with the MIAS cases. Acutance in combination with a moment-based shape measure and a Fourier descriptor-based measure gave four-group classification rate of 95% with the MIAS cases. The results indicate the importance of including lesion edge definition with shape information for classification of tumors, and that the proposed measure of acutance fills this need.

Parametric representation and screening of knee joint vibroarthrographic signals

We have been investigating analysis of knee joint vibration or vibroarthrographic (VAG) signals as a potential tool for noninvasive diagnosis and monitoring of cartilage pathology. In this paper, we present a comprehensive comparative study of different parametric representations of VAG signals. Dominant poles and cepstral coefficients were derived from autoregressive models of adaptively segmented VAG signals. Signal features and a few clinical features were used as feature vectors in pattern classification experiments based on logistic regression analysis and the leave-one-out method. The results using 51 normal and 39 abnormal signals indicated the superior performance of cepstral coefficients in VAG signal classification with an accuracy rate of 75.6%. With 51 normal and 20 abnormal signals limited to chondromalacia patella, cepstral coefficients again gave the highest accuracy rate of 85.9%.

Adaptive filtering, modelling and classification of knee joint vibroarthrographic signals for non-invasive diagnosis of articular cartilage pathology

Interpretation of vibrations or sound signals emitted from the patellofemoral joint during movement of the knee, also known as vibroarthrography (VAG), could lead to a safe, objective, and non-invasive clinical tool for early detection, localisation, and quantification of articular cartilage disorders. In this study with a reasonably large database of VAG signals of 90 human knee joints (51 normal and 39 abnormal), a new technique for adaptive segmentation based on the recursive least squares lattice (RLSL) algorithm was developed to segment the non-stationary VAG signals into locally-stationary components; the stationary components were then modelled autoregressively, using the Burg-Lattice method. Logistic classification of the primary VAG signals into normal and abnormal signals (with no restriction on the type of cartilage pathology) using only the AR coefficients as discriminant features provided an accuracy of 68.9% with the leave-one-out method. When the abnormal signals were restricted to chondromalacia patella only, the classification accuracy rate increased to 84.5%. The effects of muscle contraction interference (MCI) on VAG signals were analysed using signals from 53 subjects (32 normal and 21 abnormal), and it was found that adaptive filtering of the MCI from the primary VAG signals did not improve the classification accuracy rate. The results indicate that VAG is a potential diagnostic tool for screening for chondromalacia patella.

Improvement of sensitivity of breast cancer diagnosis with adaptive neighborhood contrast enhancement of mammograms

Mammograms are difficult to interpret, especially of cancers at their early stages. In this paper, we analyze the effectiveness of our adaptive neighborhood contrast enhancement (ANCE) technique in increasing the sensitivity of breast cancer diagnosis. Seventy-eight screen-film mammograms of 21 difficult cases (14 benign and seven malignant), 222 screen-film mammograms of 28 interval cancer patients and six benign control cases were digitized with a high-resolution of about 4096 x 2048 x 10-bit pixels and then processed with the ANCE method. Unprocessed and processed digitized mammograms as well as the original films were presented to six experienced radiologists for a receiver operating characteristic (ROC) evaluation for the difficult case set and to three reference radiologists for the interval cancer set. The results show that the radiologists' performance with the ANCE-processed images is the best among the three sets of images (original, digitized, and enhanced) in terms of area under the ROC curve and that diagnostic sensitivity is improved by the ANCE algorithm. All of the 19 interval cancer cases not detected with the original films of earlier mammographic examinations were diagnosed as malignant with the corresponding ANCE-processed versions, while only one of the six benign cases initially labeled correctly with the original mammograms was interpreted as malignant after enhancement. McNemar's tests of symmetry indicated that the diagnostic confidence for the interval cancer cases was improved by the ANCE procedure with a high level of statistical significance (p-values of 0.0001-0.005) and with no significant effect on the diagnosis of the benign control cases (p-values of 0.08-0.1). This study demonstrates the potential for improvement of diagnostic performance in early detection of breast cancer with digital image enhancement.

A segmentation-based lossless image coding method for high-resolution medical image compression

Lossless compression techniques are essential in archival and communication of medical images. In this paper, a new segmentation-based lossless image coding (SLIC) method is proposed, which is based on a simple but efficient region growing procedure. The embedded region growing procedure produces an adaptive scanning pattern for the image with the help of a very-few-bits-needed discontinuity index map. Along with this scanning pattern, an error image data part with a very small dynamic range is generated. Both the error image data and the discontinuity index map data parts are then encoded by the Joint Bi-level Image experts Group (JBIG) method. The SLIC method resulted in, on the average, lossless compression to about 1.6 h/pixel from 8 b, and to about 2.9 h/pixel from 10 b with a database of ten high-resolution digitized chest and breast images. In comparison with direct coding by JBIG, Joint Photographic Experts Group (JPEG), hierarchical interpolation (HINT), and two-dimensional Burg Prediction plus Huffman error coding methods, the SLIC method performed better by 4% to 28% on the database used.

Relationships of the vibromyogram to the surface electromyogram of the human rectus femoris muscle during voluntary isometric contraction

The relationship between vibromyographic (VMG) and electromyographic (EMG) signals during isometric contraction of the human rectus femoris muscles was studied. The method of least squares was used to obtain the best-fitting linear regression model to the root mean squared (RMS) values of the VMG and the EMG. It is shown that for the rectus femoris of four subjects, a linear VMG versus EMG relationship exists during 20-80% of the maximum voluntary contraction (MVC) at 30 degrees, 60 degrees, and 90 degrees of knee joint flexion angles. The relation between the VMG and the EMG may be explained by the order recruitment of motor units and by the "onion-skin" phenomenon of the firing rates of recruited motor units in the regulation of muscle force production as reported in electro-neurophysiologic studies.

Normal and healing ligament vascularity: a quantitative histological assessment in the adult rabbit medial collateral ligament

Normal and healing adult rabbit medial collateral ligaments (MCL) have been assessed for microvascular anatomy using a quantitative image analysis methodology. MCL preparation by ink-gelatin perfusion enabled acceptable visualisation of microvascular channels within the tissue. Fifteen adult rabbits were studied; 3 normal rabbits formed an external time-zero control group; 12 animals received a standardised gap injury to the right MCL. The ligament injury was permitted to heal for 3, 6, 17 or 40 wk (3 animals in each healing group). Results confirmed that the normal MCL is hypovascular (about 1.46% vascularity by area) and that microvascular channels are highly organised and oriented longitudinally deep within the tissue. Healing MCL scar becomes twice as vascular as normal ligament early on, but returns to near normal values by 40 wk. Microvascular channels appear less organised in scar than in contralateral controls, but remodel with time. The directional scatter and spatial extent of ligament microvascular channels is quantifiable in normal and healing tissues.

Screening of vibroarthrographic signals via adaptive segmentation and linear prediation modeling

This paper proposes a noninvasive method to diagnose chondromalacia patella at its early stages by recording knee vibration signals (also known as vibroarthrographic or VAG signals) over the mid-patella during normal movement. An adaptive segmentation method was developed to segment the nonstationary VAG signals. The least squares modeling method was used to reduce the number of data samples to a few model parameters. Model parameters along with a few clinical parameters and a signal variability parameter were then used as discriminant features for screening VAG signals by applying logistic and discriminant algorithms. The system was trained using ten normal and eight abnormal signals. It correctly screened a separate test set of ten normal and eight abnormal signals except for one normal signal. The proposed method should find use as an alternative technique for diagnosis of knee joint pathology or as a test before arthroscopy or major knee surgery.

Localization of knee joint cartilage pathology by multichannel vibroarthrography

This paper proposes non-invasive techniques to localize sound or vibroarthrographic (VAG) signal sources in human knee joints. VAG signals from normal subjects, patients who subsequently underwent arthroscopy, and cadavers with arthroscopically-created lesions, obtained by stimulation with a finger tap over the mid-patella and swinging movement of the leg, were analyzed for time delays using cross-correlation functions for source localization. Correct results were obtained for 13 of the 14 subjects tested by finger stimulation, and for 11 of the 12 subjects whose VAG signals during swinging movement were analyzed. The techniques could be valuable in the diagnosis and treatment of knee pathology before and after joint surgery or drug therapy.

Image restoration by adaptive-neighborhood noise subtraction

A new algorithm for image restoration in the presence of additive white Gaussian noise is presented. This algorithm is based on a new, adaptive method to estimate the additive noise. The basic idea in this technique is to identify uniform structures or objects in the image by use of an adaptive neighborhood and to estimate the noise and the signal content in these areas separately. The noise is then subtracted selectively from the seed pixel of the adaptive neighborhood, and the process is repeated at every pixel in the image. The algorithm is compared with the adaptive two-dimensional least-mean-squares and the adaptive rectangular-window least-mean-squares algorithms for noise suppression. The results from the application of these algorithms to synthesized images and natural scenes are presented along with mean-squared-error measures. The new algorithm performs better than the other two methods both in terms of visual presentation and mean-squared error.

Adaptive cancellation of muscle contraction interference in vibroarthrographic signals

Vibroarthrography (VAG) is an innovative, objective, non-invasive technique for obtaining diagnostic information concerning the articular cartilage of a joint. Knee VAG signals can be detected using a contact sensor over the skin surface of the knee joint during knee movement such as flexion and/or extension. These measured signals, however, contain significant interference caused by muscle contraction that is required for knee movement. Quality improvement of VAG signals is an important subject, and crucial in computer-aided diagnosis of cartilage pathology. While simple frequency domain high-pass (or band-pass) filtering could be used for minimizing muscle contraction interference (MCI), it could eliminate possible overlapping spectral components of the VAG signals. In this work, an adaptive MCI cancellation technique is presented as an alternative technique for filtering VAG signals. Methods of measuring the VAG and reference signals (MCI) are described, with details on MCI identification, characterization, and step size optimization for the adaptive filter. The performance of the method is evaluated by simulated signals as well as signals obtained from human subjects under isotonic contraction.

Application of shape analysis to mammographic calcifications

The authors have developed a set of shape factors to measure the roughness of contours of calcifications in mammograms and for use in their classification as malignant or benign. The analysis of mammograms is performed in three stages. First, a region growing technique is used to obtain the contours of calcifications. Then, three measures of shape features, including compactness, moments, and Fourier descriptors are computed for each region. Finally, their applicability for classification is studied by using the three shape measures to form feature vectors. Classification of 143 calcifications from 18 biopsy-proven cases as benign or malignant using the three measures with the nearest-neighbor method was 100% accurate.

Two-dimensional restoration of single photon emission computed tomography images using the Kalman filter

The discrete filtered backprojection (DFBP) algorithm used for the reconstruction of single photon emission computed tomography (SPECT) images affects image quality because of the operations of filtering and discretization. The discretization of the filtered backprojection process can cause the modulation transfer function (MTF) of the SPECT imaging system to be anisotropic and nonstationary, especially near the edges of the camera's field of view. The use of shift-invariant restoration techniques fails to restore large images because these techniques do not account for such variations in the MTF. This study presents the application of a two-dimensional (2D) shift-variant Kalman filter for post-reconstruction restoration of SPECT slices. This filter was applied to SPECT images of a hollow cylinder phantom; a resolution phantom; and a large, truncated cone phantom containing two types of cold spots, a sphere, and a triangular prism. The images were acquired on an ADAC GENESYS camera. A comparison was performed between results obtained by the Kalman filter and those obtained by shift-invariant filters. Quantitative analysis of the restored images performed through measurement of root mean squared errors shows a considerable reduction in error of Kalman-filtered images over images restored using shift-invariant methods.

A comparative study of simultaneous vibromyography and electromyography with active human quadriceps

Vibromyographic (VMG) signals, which are low-frequency vibration signals generated during muscle contraction, were studied in comparison with electromyographic (EMG) signals recorded simultaneously during isometric contraction of the human quadriceps muscles. The comparison was accomplished by evaluating the averaged root mean squared (rms) value, mean frequency (MF), and peak frequency (PF) of the VMG and EMG signals for four muscle contraction levels at joint angles of 30 degrees, 60 degrees, and 90 degrees. The four contraction levels, namely 20, 40, 60, and 80% of maximum voluntary contraction (MVC), were estimated and controlled by the torque readings of a Cybex II dynamometer. It was found that the VMG and EMG under the same conditions on the same muscle group are in general equally sensitive to the levels of muscle contraction. Results show that the rms value of the VMG signal increases linearly, in a manner similar to the EMG rms/%MVC relationship, with increasing muscle contraction levels. Furthermore, the study indicates that the averaged MF (6-24 Hz) and PF (9-19 Hz) of the VMG signals are much lower than the MF (75-109 Hz) and PF (40-80 Hz) of the EMG signals. The slopes of MF/%MVC curves for the VMG and EMG are approximately the same for 60 degrees and 90 degrees joint angles (approximately 3.1 Hz per 20% MVC for VMG and approximately 2.6 Hz per 20% MVC for EMG).(ABSTRACT TRUNCATED AT 250 WORDS)

Analysis of knee vibration signals using linear prediction

Clinical methods used at present for the diagnosis of cartilage pathology in the knee are invasive in nature, and carry some risks. There exists a need for the development of a safe, objective, noninvasive method for early detection, localization, and quantification of cartilage pathology in the knee. This paper investigates the possibility of developing such a method based on an analysis of vibrations produced by joint surfaces rubbing against one another during normal movement. In particular, the method of modeling by linear prediction is used for adaptive segmentation and parameterization of knee vibration signals. Dominant poles are extracted from the model system function for each segment based on their energy contributions and bandwidths. These dominant poles represent the dominant features of the signal segments in the spectral domain. Two-dimensional feature vectors are then constructed using the first dominant pole and the ratio of power in the 40-120 Hz band to the total power of the segment. The potential use of this method to distinguish between vibrations produced by normal volunteers and patients known to have cartilage pathology (chondromalacia) is discussed.

Mathematical modeling and spectrum analysis of the physiological patello-femoral pulse train produced by slow knee movement

Analysis of vibration signals emitted by the knee joint has the potential for the development of a noninvasive procedure for the diagnosis and monitoring of knee pathology. In order to obtain as much information as possible from the power density spectrum of the knee vibration signal, it is necessary to identify the physiological factors (or physiologically relevant parameters) that shape the spectrum. This paper presents a mathematical model for knee vibration signals, in particular the physiological patello-femoral pulse (PFP) train produced by slow knee movement. It demonstrates through the mathematical model that the repetition rate of the physiological PFP train introduces repeated peaks in the power spectrum, and that it affects the spectrum mainly at low frequencies. The theoretical results also show that the spectral peaks at multiples of the PFP repetition rate become more evident when the variance of the interpulse interval (IPI) is small, and that these spectral peaks shift toward higher frequencies with increasing PFP repetition rates. To evaluate the mathematical model, a simulation algorithm was developed, which generates PFP signals with adjustable repetition rate and IPI variance. Signals generated by simulation were seen to possess representative spectral characteristics typically observed in physiological PFP signals. This simulation procedure allows an interactive examination of several factors which affect the PFP train spectrum. Finally, in vivo measurements of physiological PFP signals of normal volunteers are presented. Results of simulations and analysis of signals recorded from human subjects support the mathematical model's prediction that the IPI statistics play a very significant role in determining the low-end power spectrum of the physiological PFP signal.(ABSTRACT TRUNCATED AT 250 WORDS)

Quantitative analysis of the fine vascular anatomy of articular ligaments

An image analysis technique has been developed to quantitatively describe the fine vascular patterns observed in ligament tissue. The longitudinal orientational distribution and total vessel volume of India-ink-perfused blood vessel segments in normal and healing ligaments were determined. The methods involved special vascular preparation of adult rabbit knee medial collateral ligaments (MCL) by India-ink perfusion. Black and white microscope images of ink-perfused tissue sections were subjected to a thresholding procedure to binarize digitized ligament images, which were then skeletonized and analyzed for directional distribution based on the least-squares technique. Analysis of medial collateral ligaments in New Zealand White rabbits using this method has shown that scarred tissue is more vascular and has a more chaotic angular distribution of blood-vessel segments than normal ligament tissue.

Region-based contrast enhancement of mammograms

Diagnostic features in mammograms vary widely in size and shape. Classical image enhancement techniques cannot adapt to the varying characteristics of such features. An adaptive method for enhancing the contrast of mammographic features of varying size and shape is presented. The method uses each pixel in the image as a seed to grow a region. The extent and shape of the region adapt to local image gray-level variations, corresponding to an image feature. The contrast of each region is calculated with respect to its individual background. Contrast is then enhanced by applying an empirical transformation based on each region's seed pixel value, its contrast, and its background. A quantitative measure of image contrast improvement is also defined based on a histogram of region contrast and used for comparison of results. Using mammogram images digitized at high resolution (less than 0.1 mm pixel size), it is shown that the validity of microcalcification clusters and anatomic details is considerably improved in the processed images.

Performance analysis of reversible image compression techniques for high-resolution digital teleradiology

The performances of a number of block-based, reversible, compression algorithms suitable for compression of very-large-format images (4096x4096 pixels or more) are compared to that of a novel two-dimensional linear predictive coder developed by extending the multichannel version of the Burg algorithm to two dimensions. The compression schemes implemented are: Huffman coding, Lempel-Ziv coding, arithmetic coding, two-dimensional linear predictive coding (in addition to the aforementioned one), transform coding using discrete Fourier-, discrete cosine-, and discrete Walsh transforms, linear interpolative coding, and combinations thereof. The performances of these coding techniques for a few mammograms and chest radiographs digitized to sizes up to 4096x4096 10 b pixels are discussed. Compression from 10 b to 2.5-3.0 b/pixel on these images has been achieved without any loss of information. The modified multichannel linear predictor outperforms the other methods while offering certain advantages in implementation.

Preconstruction restoration of myocardial single photon emission computed tomography images

A restoration scheme for single photon emission computed tomography (SPECT) images that performs restoration before reconstruction (preconstruction restoration) from planar (projection) images is presented. A comparison is performed between results obtained in this study and those obtained by a method reported previously where the restoration is performed after reconstruction (postreconstruction restoration). The filters investigated are the Wiener and power spectrum equalization filters. These filters are applied to SPECT images of a hollow cylinder phantom and a cardiac phantom acquired on a Siemens Rota camera. Quantitative analyses of the results are performed through measurements of contrast ratios and root mean squared errors. The preconstruction restored images show a significant decrease in the root mean squared error and an increase in contrast over the postconstruction restored images.

High-resolution digital teleradiology: a perspective

Teleradiology has come a long way, from analog transmission systems using slow-scan television over standard telephone lines, to present-day, commercially available, microcomputer-based, low-resolution teleradiology systems. However, there exists a need to address the high-resolution end of the medical imaging categories, namely chest radiographs and mammograms, to firmly establish teleradiology. The availability of high-resolution image digitizers, display units, and digital hard copiers has made high-resolution digital teleradiology a feasible concept. Although the use of satellite channels can speed up the transmission of radiographic image data, with widespread acceptance of high-resolution teleradiology systems in the foreseeable future, the sheer amount of data involved in this field will give rise to problems of data transmission and storage. Data compression schemes can bring down the amount of data handled and can have a great economic impact on future teleradiology systems. We have developed a number of compression techniques for reversible compression of medical images. Our experiments have shown that lossless compression of the order of 4:1 is possible for a class of high-resolution medical images. Use of pattern recognition techniques offers the potential to bring down these data rates even further. We plan to use these techniques in a prototype high-resolution teleradiology system being developed. In this paper, we trace some of the developments in teleradiology and image data compression, and present a perspective for teleradiology in the 1990s.

Statistical analysis of collagen alignment in ligaments by scale-space analysis

Injuries to ligaments in the knee are common in sports and other physical activities. Some clinical methods are available for qualitatively evaluating the degree of ligament injury and healing. It is, however, desirable to objectively assess the healing of ligaments and to predicate optimal treatment on quantitative measurements of their structure. Information such as areas of coverage and spatial orientations of collagen fibrils, for example, may provide important information about the internal structure of ligament tissues. Since normal ligament tissues are made up of collagen fibrils which are highly organized, they can be considered as oriented piecewise linear patterns. In this paper, we propose a computational technique for statistical analysis of collagen alignment in ligament images using the scale-space approach. In this method, a ligament image is preprocessed by a sequence of filters which are second derivatives of two-dimensional Gaussian functions with different scales. This gives a set of zero-crossing maps (the scale space) from which a stability map is generated. Significant linear patterns are captured by analyzing the stability map. The directional information in terms of orientation distributions of the collagen fibrils in the image and the area covered by the fibrils in specific directions are extracted for statistical analysis. Examples illustrating the performance of this method with scanning electron microscope images of the collagen fibrils in healing rabbit medial collateral ligaments are presented in this paper.

Restoration of gamma camera-based nuclear medicine images

Experiments were conducted using a Siemens Rota camera to study the applicability of two linear shift-invariant (LSI) filters, namely, the Wiener and power spectrum equalization filters, for restoration of planar projections and single-photon-emission computed tomography (SPECT) images. In the restoration scheme, the system transfer function, computed from a line source image, is modeled by a 2-D Gaussian function. The noise power spectrum is modeled as a constant for planar images and as a ramp for SPECT images. The filters have been applied to restore computer-simulated 1-D and 2-D projections and SPECT images of two simple phantoms, 2-D projections of two phantoms obtained from the Siemens Rota camera, and SPECT images of a cardiac phantom obtained from the Siemens Rota camera. The filters are shown to perform partial restoration. Considerable noise suppression and detail enhancement have been observed in the restored images. quantitative measurements such as root-mean-squared error and contrast ratio have been used for objective analysis of the results, which are encouraging.