Wavelets in temporal and spatial processing of biomedical images

Prediction Model of Residual Neural Network for Pathological Confirmed Lymph Node Metastasis of Ovarian Cancer

Purpose. We want to develop a model for predicting lymph node status based on positron emission computed tomography (PET) images of untreated ovarian cancer patients. We use the feature map formed by wavelet transform and the parameters obtained by image segmentation to build the model. The model is expected to help clinicians and provide additional information about what to do with first-visit patients. Materials and Methods. Our study included 224 patients with ovarian cancer. We have chosen two main methods to extract information from images. On the one hand, we segmented the image to extract the parameters to evaluate the clustering effect. On the other hand, we used wavelet transform to extract the image’s texture information to form the image’s feature map. Based on the above two kinds of information, we used residual neural network and support vector machine for modeling. Results. We established a model to predict lymph node metastasis in patients with primary ovarian cancer using PET images. On the training set, our accuracy was 0.8854, AUC: 0.9472, CI: 0.9098-0.9752, sensitivity was 0.9865, and specificity was 0.7952. On the test set, our accuracy was 0.9104, AUC: 0.9259, CI: 0.8417-0.9889, sensitivity was 0.8125, and specificity was 1.0000. Conclusions. We used wavelet transform to process the preoperative medical images of ovarian cancer patients, and the residual neural network can effectively predict the lymph node metastasis of ovarian cancer patients, which is undoubted of great significance for patients’ staging and treatment options.

A preliminary study of deep learning-based reconstruction specialized for denoising in high-frequency domain: usefulness in high-resolution three-dimensional magnetic resonance cisternography of the cerebellopontine angle

PURPOSE

Deep learning-based reconstruction (DLR) has been developed to reduce image noise and increase the signal-to-noise ratio (SNR). We aimed to evaluate the efficacy of DLR for high spatial resolution (HR)-MR cisternography.

METHODS

This retrospective study included 35 patients who underwent HR-MR cisternography. The images were reconstructed with or without DLR. The SNRs of the CSF and pons, contrast of the CSF and pons, and sharpness of the normal-side trigeminal nerve using full width at half maximum (FWHM) were compared between the two image types. Noise quality, sharpness, artifacts, and overall image quality of these two types of images were qualitatively scored.

RESULTS

The SNRs of the CSF and pons were significantly higher with DLR than without DLR (CSF 21.81 ± 7.60 vs. 15.33 ± 4.03, p < 0.001; pons 5.96 ± 1.38 vs. 3.99 ± 0.48, p < 0.001). There were no significant differences in the contrast of the CSF and pons (p = 0.225) and sharpness of the normal-side trigeminal nerve using FWHM (p = 0.185) without and with DLR, respectively. Noise quality and the overall image quality were significantly higher with DLR than without DLR (noise quality 3.95 ± 0.19 vs. 2.53 ± 0.44, p < 0.001; overall image quality 3.97 ± 0.17 vs. 2.97 ± 0.12, p < 0.001). There were no significant differences in sharpness (p = 0.371) and artifacts (p = 1) without and with DLR.

CONCLUSION

DLR can improve the image quality of HR-MR cisternography by reducing image noise without sacrificing contrast or sharpness.

Higher Sensitivity and Reproducibility of Wavelet-Based Amplitude of Resting-State fMRI

The fast Fourier transform (FFT) is a widely used algorithm used to depict the amplitude of low-frequency fluctuation (ALFF) of resting-state functional magnetic resonance imaging (RS-fMRI). Wavelet transform (WT) is more effective in representing the complex waveform due to its adaptivity to non-stationary or local features of data and many varieties of wavelet functions with different shapes being available. However, there is a paucity of RS-fMRI studies that systematically compare between the results of FFT versus WT. The present study employed five cohorts of datasets and compared the sensitivity and reproducibility of FFT-ALFF with those of Wavelet-ALFF based on five mother wavelets (namely, db2, bior4.4, morl, meyr, and sym3). In addition to the conventional frequency band of 0.0117-0.0781 Hz, a comparison was performed in sub-bands, namely, Slow-6 (0-0.0117 Hz), Slow-5 (0.0117-0.0273 Hz), Slow-4 (0.0273-0.0742 Hz), Slow-3 (0.0742-0.1992 Hz), and Slow-2 (0.1992-0.25 Hz). The results indicated that the Wavelet-ALFF of all five mother wavelets was generally more sensitive and reproducible than FFT-ALFF in all frequency bands. Specifically, in the higher frequency band Slow-2 (0.1992-0.25 Hz), the mean sensitivity of db2-ALFF results was 1.54 times that of FFT-ALFF, and the reproducibility of db2-ALFF results was 2.95 times that of FFT-ALFF. The findings suggest that wavelet-ALFF can replace FFT-ALFF, especially in the higher frequency band. Future studies should test more mother wavelets on other RS-fMRI metrics and multiple datasets.

Dynamic positron emission tomography restoration with low-rank representation incorporating edge preservation

BACKGROUND

Dynamic positron emission tomography (PET) is a powerful tool that provides useful quantitative information on physiological and biochemical processes. However, the low signal-to-noise ratio (SNR) in short dynamic frames is a challenge.

OBJECTIVE

To get high SNR in the dynamic PET and to achieve high-quality PET parametric image are the objective of this study.

METHODS

Low-rank (LR) modeling and edge-preserving prior are incorporated in this study with a unified mathematical framework to improve the SNR of a dynamic PET image series. The proposed algorithm is designed to reduce noise in homogeneous areas while preserving the edges of regions of interest.

RESULTS

The performance of the proposed method (LRH) is compared both visually and quantitatively by using the classic Gaussian filter and an LR expression filter on a digital brain phantom and in vivo rat study. Experimental results demonstrate that the proposed filter can achieve superior visual and quantitative performance without sacrificing spatial resolution.

CONCLUSIONS

The proposed LRH is considerably effective and exhibits great potential in processing dynamic PET data with high noise levels.

Wavelets and statistical analysis of functional magnetic resonance images of the human brain

Wavelets provide an orthonormal basis for multiresolution analysis and decorrelation or ‘whitening’ of nonstationary time series and spatial processes. Wavelets are particularly well suited to analysis of biological signals and images, such as human brain imaging data, which often have fractal or scale-invariant properties. We briefly define some key properties of the discrete wavelet transform (DWT) and review its applications to statistical analysis of functional magnetic resonance imaging (fMRI) data. We focus on time series resampling by ‘wavestrapping’ of wavelet coefficients, methods for efficient linear model estimation in the wavelet domain, and wavelet-based methods for multiple hypothesis testing, all of which are somewhat simplified by the decorrelating property of the DWT.

Choosing Wavelet Methods, Filters, and Lengths for Functional Brain Network Construction

Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands. Using these time series, one can estimate frequency-band specific functional connectivity between sensors or regions of interest, and thereby construct functional brain networks that can be examined from a graph theoretic perspective. Despite their common use, however, practical guidelines for the choice of wavelet method, filter, and length have remained largely undelineated. Here, we explicitly explore the effects of wavelet method (MODWT vs. DWT), wavelet filter (Daubechies Extremal Phase, Daubechies Least Asymmetric, and Coiflet families), and wavelet length (2 to 24)—each essential parameters in wavelet-based methods—on the estimated values of graph metrics and in their sensitivity to alterations in psychiatric disease. We observe that the MODWT method produces less variable estimates than the DWT method. We also observe that the length of the wavelet filter chosen has a greater impact on the estimated values of graph metrics than the type of wavelet chosen. Furthermore, wavelet length impacts the sensitivity of the method to detect differences between health and disease and tunes classification accuracy. Collectively, our results suggest that the choice of wavelet method and length significantly alters the reliability and sensitivity of these methods in estimating values of metrics drawn from graph theory. They furthermore demonstrate the importance of reporting the choices utilized in neuroimaging studies and support the utility of exploring wavelet parameters to maximize classification accuracy in the development of biomarkers of psychiatric disease and neurological disorders.

Multi-scale classification of disease using structural MRI and wavelet transform

Recently, multivariate analysis algorithms have become a popular tool to diagnose neurological diseases based on neuroimaging data. Most studies, however, are biased for one specific scale, namely the scale given by the spatial resolution (i.e. dimension) of the data. In the present study, we propose to use the dual-tree complex wavelet transform to extract information on different spatial scales from structural MRI data and show its relevance for disease classification. Based on the magnitude representation of the complex wavelet coefficients calculated from the MR images, we identified a new class of features taking scale, directionality and potentially local information into account simultaneously. By using a linear support vector machine, these features were shown to discriminate significantly between spatially normalized MR images of 41 patients suffering from multiple sclerosis and 26 healthy controls. Interestingly, the decoding accuracies varied strongly among the different scales and it turned out that scales containing low frequency information were partly superior to scales containing high frequency information. Usually, this type of information is neglected since most decoding studies use only the original scale of the data. In conclusion, our proposed method has not only a high potential to assist in the diagnostic process of multiple sclerosis, but can be applied to other diseases or general decoding problems in structural or functional MRI.

Brain perfusion heterogeneity measurement based on Random Walk algorithm: choice and influence of inner parameters

A Random Walk (RW) algorithm was designed to quantify the level of diffuse heterogeneous perfusion in brain SPECT images in patients suffering from systemic brain disease or from drug-induced therapy. The goal of the present paper is to understand the behavior of the RW method on different kinds of images (extrinsic parameters) and also to understand how to choose the right parameters of the RW (intrinsic parameters) depending on the image characteristics (i.e. SPECT images). "Extrinsic parameters" are related to the image characteristics (level/size of defect and diffuse heterogeneity) and "intrinsic" parameters are related to the parameters of the method (number (N(rw)) and length of walk (L(rw)), temperature (T) and slowing parameter (S)). Two successive studies were conducted to test the influence of these parameters on the RW result. In the first study, calibrated checkerboard images are used to test the influence of "extrinsic parameters" (i.e. image characteristics) on the RW result (R-value). The R-value was tested as a function of (i) the size of black & white (B&W) squares simulating the size of a cortical defect, (ii) the intensity level gaps between the B&W squares simulating the intensity of the cortical defect and (iii) intensity (=variance) of noise, simulating the diffuse heterogeneity. The second study was constructed with simulated representative brain SPECT images, to test the "intrinsic" parameters. The R-value was tested regarding the influence of four parameters: S, T, N(rw) and L(rw). The third study is constructed so as to see if the classification by diffuse heterogeneity of real brain SPECT images is the same if it's made by senior clinicians or by RW algorithm.

RESULTS

Study 1: the RW was strongly influenced by all the characteristics of the images. Moreover, these characteristics interact with each other. The RW is influenced most by diffuse heterogeneity, then by intensity and finally by the size of a defect. Study 2: N(rw) and L(rw) values of 1000 give an optimal reproducibility of the measurement (mean standard deviation<0.1), a fast computation time (time<0.5s/image) and have a maximum difference in terms of R-value between the two extreme images corresponding to the range of the population studied. The best S and T values for SPECT images are 3 and 15, respectively. Study 3: A significant correlation was found between RW ranking and the physicians' consensus (rho=0.789; p<0.0001).

CONCLUSION

This study confirms that the RW method is able to measure the heterogeneity of brain SPECT images even in the presence of a large defect. However, the result of the method is strongly influenced by the "intrinsic" parameters, so the program should be calibrated for each different type of image.

Active mask segmentation of fluorescence microscope images

We propose a new active mask algorithm for the segmentation of fluorescence microscope images of punctate patterns. It combines the (a) flexibility offered by active-contour methods, (b) speed offered by multiresolution methods, (c) smoothing offered by multiscale methods, and (d) statistical modeling offered by region-growing methods into a fast and accurate segmentation tool. The framework moves from the idea of the "contour" to that of "inside and outside," or masks, allowing for easy multidimensional segmentation. It adapts to the topology of the image through the use of multiple masks. The algorithm is almost invariant under initialization, allowing for random initialization, and uses a few easily tunable parameters. Experiments show that the active mask algorithm matches the ground truth well and outperforms the algorithm widely used in fluorescence microscopy, seeded watershed, both qualitatively, as well as quantitatively.

Wavelet method for CT colonography computer-aided polyp detection

Computed tomographic colonography (CTC) computer aided detection (CAD) is a new method to detect colon polyps. Colonic polyps are abnormal growths that may become cancerous. Detection and removal of colonic polyps, particularly larger ones, has been shown to reduce the incidence of colorectal cancer. While high sensitivities and low false positive rates are consistently achieved for the detection of polyps sized 1 cm or larger, lower sensitivities and higher false positive rates occur when the goal of CAD is to identify "medium"-sized polyps, 6-9 mm in diameter. Such medium-sized polyps may be important for clinical patient management. We have developed a wavelet-based postprocessor to reduce false positives for this polyp size range. We applied the wavelet-based postprocessor to CTC CAD findings from 44 patients in whom 45 polyps with sizes of 6-9 mm were found at segmentally unblinded optical colonoscopy and visible on retrospective review of the CT colonography images. Prior to the application of the wavelet-based postprocessor, the CTC CAD system detected 33 of the polyps (sensitivity 73.33%) with 12.4 false positives per patient, a sensitivity comparable to that of expert radiologists. Fourfold cross validation with 5000 bootstraps showed that the wavelet-based postprocessor could reduce the false positives by 56.61% (p <0.001), to 5.38 per patient (95% confidence interval [4.41, 6.34]), without significant sensitivity degradation (32/45, 71.11%, 95% confidence interval [66.39%, 75.74%], p=0.1713). We conclude that this wavelet-based postprocessor can substantially reduce the false positive rate of our CTC CAD for this important polyp size range.

Medical image noise reduction using the Sylvester-Lyapunov equation

Multiplicative noise is often present in medical and biological imaging, such as magnetic resonance imaging (MRI), Ultrasound, positron emission tomography (PET), single photon emission computed tomography (SPECT), and fluorescence microscopy. Noise reduction in medical images is a difficult task in which linear filtering algorithms usually fail. Bayesian algorithms have been used with success but they are time consuming and computationally demanding. In addition, the increasing importance of the 3-D and 4-D medical image analysis in medical diagnosis procedures increases the amount of data that must be efficiently processed. This paper presents a Bayesian denoising algorithm which copes with additive white Gaussian and multiplicative noise described by Poisson and Rayleigh distributions. The algorithm is based on the maximum a posteriori (MAP) criterion, and edge preserving priors which avoid the distortion of relevant anatomical details. The main contribution of the paper is the unification of a set of Bayesian denoising algorithms for additive and multiplicative noise using a well-known mathematical framework, the Sylvester-Lyapunov equation, developed in the context of the Control theory.

PET kinetic analysis: wavelet denoising of dynamic PET data with application to parametric imaging

Physiological functions (e.g., cerebral blood flow, glucose metabolism, and neuroreceptor binding) can be investigated as parameters estimated by kinetic modeling using dynamic positron emission tomography (PET) images. Imaging of these physiological parameters, called parametric imaging, can locate the regional distribution of functionalities. However, the most serious technical issue affecting parametric imaging is noise in dynamic PET data. This review describes wavelet denoising of dynamic PET images for improving image quality in estimated parametric images. Wavelet denoising provides significantly improved quality directly to dynamic PET images and indirectly to estimated parametric images. The application of wavelet denoising to radio-ligand and kinetic analysis is still in the development stage, but even so, it is thought that wavelet techniques will have a substantial impact on nuclear medicine in the near future.

Multiscale analysis of MR-mammography data

In this work we propose a method for automatically discriminating between different types of tissue in MR mammography datasets. This is accomplished by employing a wavelet-based multiscale analysis. After the data has been wavelet-transformed unsupervised machine learning methods are employed to identify typical patterns in the wavelet domain. To demonstrate the potential of the proposed approach we apply a filtering procedure that extracts the wavelet-based image information related to tumour tissue. In this way we obtain a robust segmentation of suspicious tissue in the MR image.

Diffusional trapping of GluR1 AMPA receptors by input-specific synaptic activity

Synaptic activity regulates the postsynaptic accumulation of AMPA receptors over timescales ranging from minutes to days. Indeed, the regulated trafficking and mobility of GluR1 AMPA receptors underlies many forms of synaptic potentiation at glutamatergic synapses throughout the brain. However, the basis for synapse-specific accumulation of GluR1 is unknown. Here we report that synaptic activity locally immobilizes GluR1 AMPA receptors at individual synapses. Using single-molecule tracking together with the silencing of individual presynaptic boutons, we demonstrate that local synaptic activity reduces diffusional exchange of GluR1 between synaptic and extraynaptic domains, resulting in postsynaptic accumulation of GluR1. At neighboring inactive synapses, GluR1 is highly mobile with individual receptors frequently escaping the synapse. Within the synapse, spontaneous activity confines the diffusional movement of GluR1 to restricted subregions of the postsynaptic membrane. Thus, local activity restricts GluR1 mobility on a submicron scale, defining an input-specific mechanism for regulating AMPA receptor composition and abundance.

DWT-DCT hybrid scheme for medical image compression

With the development of communication technology the applications and services of health telemetics are growing. In view of the increasingly important role played by digital medical imaging in modern health care, it is necessary for large amount of image data to be economically stored and/or transmitted. There is a need for the development of image compression systems that combine high compression ratio with preservation of critical information. During the past decade wavelets have been a significant development in the field of image compression. In this paper, a hybrid scheme using both discrete wavelet transform (DWT) and discrete cosine transform (DCT) for medical image compression is presented. DCT is applied to the DWT details, which generally have zero mean and small variance, thereby achieving better compression than obtained from either technique alone. The results of the hybrid scheme are compared with JPEG and set partitioning in hierarchical trees (SPIHT) coder and it is found that the performance of the proposed scheme is better.

Medical Image Compression using Wavelet Transform on Mobile Devices with ROI coding support

Medical applications have already been integrated into mobile devices (e.g. Tablet PC's and PDA's) and are being used by medical personnel in treatment centers, for retrieving and examining patient data and medical images. Network transmission and image data processing are key issues in such platforms, due to the significant image file sizes. Wavelet transform has been considered to be a highly efficient technique of image compression resulting in both lossless and lossy compressed images of great accuracy, enabling its use on medical images. This paper discusses a Picture Archiving and Communication Systems (PACS) application designed for viewing DICOM compliant medical images using Wavelet compression with ROI coding support, on mobile devices. In addition, it presents initial results from its pilot application and demonstrates its performance over heterogeneous radio network segments, like IEEE 802.11b, GPRS and DVB-H.

Use of wavelet and fast Fourier transforms in pharmacodynamics

Progress has been made in the development and application of mechanism-based pharmacodynamic models for describing the drug-specific and physiological factors influencing the time course of responses to the diverse actions of drugs. However, the biological variability in biosignals and the complexity of pharmacological systems often complicate or preclude the direct application of traditional structural and nonstructural models. Mathematical transforms may be used to provide measures of drug effects, identify structural and temporal patterns, and visualize multidimensional data from analyses of biomedical signals and images. Fast Fourier transform (FFT) and wavelet analyses are two methodologies that have proven to be useful in this context. FFT converts a signal from the time domain to the frequency domain, whereas wavelet transforms colocalize in both domains and may be utilized effectively for nonstationary signals. Nonstationary drug effects are common but have not been well analyzed and characterized by other methods. In this review, we discuss specific applications of these transforms in pharmacodynamics and their potential role in ascertaining the dynamics of spatiotemporal properties of complex pharmacological systems.

A novel 3D wavelet-based filter for visualizing features in noisy biological data

Summary We have developed a three-dimensional (3D) wavelet-based filter for visualizing structural features in volumetric data. The only variable parameter is a characteristic linear size of the feature of interest. The filtered output contains only those regions that are correlated with the characteristic size, thus de-noising the image. We demonstrate the use of the filter by applying it to 3D data from a variety of electron microscopy samples, including low-contrast vitreous ice cryogenic preparations, as well as 3D optical microscopy specimens.

Identification of plasma membrane macro- and microdomains from wavelet analysis of FRET microscopy

In this study, we sought to characterize functional signaling domains by applying the multiresolution properties of the continuous wavelet transform to fluorescence resonance energy transfer (FRET) microscopic images of plasma membranes. A genetically encoded FRET reporter of protein kinase C (PKC)-dependent phosphorylation was expressed in COS1 cells. Differences between wavelet coefficient matrices revealed several heterogeneous domains (typically ranging from 1 to 5 microm), reflecting the dynamic balance between PKC and phosphatase activity during stimulation with phorbol-12,13-dibutyrate or acetylcholine. The balance in these domains was not necessarily reflected in the overall plasma membrane changes, and observed heterogeneity was absent when cells were exposed to a phosphatase or PKC inhibitor. Prolonged exposure to phorbol-12,13-dibutyrate and acetylcholine yielded more homogeneous FRET distribution in plasma membranes. The proposed wavelet-based image analysis provides, for the first time, a basis and a means of detecting and quantifying dynamic changes in functional signaling domains, and may find broader application in studying fine aspects of cellular signaling by various imaging reporters.

Wavelets and functional magnetic resonance imaging of the human brain

The discrete wavelet transform (DWT) is widely used for multiresolution analysis and decorrelation or "whitening" of nonstationary time series and spatial processes. Wavelets are naturally appropriate for analysis of biological data, such as functional magnetic resonance images of the human brain, which often demonstrate scale invariant or fractal properties. We provide a brief formal introduction to key properties of the DWT and review the growing literature on its application to fMRI. We focus on three applications in particular: (i) wavelet coefficient resampling or "wavestrapping" of 1-D time series, 2- to 3-D spatial maps and 4-D spatiotemporal processes; (ii) wavelet-based estimators for signal and noise parameters of time series regression models assuming the errors are fractional Gaussian noise (fGn); and (iii) wavelet shrinkage in frequentist and Bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps. We conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fMRI data.

A preliminary report on the role of spatial frequency analysis in the perception of breast cancers missed at mammography screening

RATIONALE AND OBJECTIVES

Because several factors are involved in cancer detection, a malignant lesion that is visible on a mammogram will not necessarily be reported by the radiologist reading the case. Indeed, a significant fraction of screening-detected cancers are visible in retrospect, and were perceived by the radiologist when the case was read, but were either reported as benign findings or dismissed as variations of normal breast tissue. In this preliminary report the spatial frequency characteristics of clinically missed lesions are investigated by analyzing the mammogram acquired when the lesion was sent for biopsy and the most recent prior mammogram. For control purposes, the contralateral breast is also analyzed, when this breast is lesion free.

MATERIALS AND METHODS

A database of 70 mammogram cases was assembled. Each case contained eight films: craniocaudal (CC) and mediolateral oblique (MLO) of the breast where a biopsy-proven lesion was found, CC and MLO of the contralateral breast, and CC and MLO of both breasts in the most recent prior mammogram. The dictated reports for all of these cases were obtained. Both benign and malignant lesions were used. The films were digitized and an region of interest surrounding each lesion was segmented from the image for processing using wavelet packets to extract spatial frequency information. The corresponding area was also segmented from the prior mammogram and from the contralateral breast, when this breast was lesion-free. Analysis of variance was used to determine if statistically significant differences existed between the derived features of cancer in the current and prior mammograms.

RESULTS

The data suggests that malignant lesions reported in the prior mammogram as being benign differed from correctly reported malignant lesions and from correctly reported benign lesions. They also differed from nonreported malignant lesions. In addition, the spatial frequency representation of cancer significantly differed in the current and prior cases from the representation of normal breast tissue.

CONCLUSION

Spatial frequency analysis may be useful to differentiate malignant lesions that are reported as benign and correctly reported benign lesions.

Brain mapping: new wave optical imaging

Optical imaging of intrinsic signals is widely used for high-resolution brain mapping in various animal species. A new approach using continuous data acquisition and Fourier decomposition of the signal allows for much faster mapping, opening up the possibility of applying this method to new experimental questions.

Complex wavelets for extended depth-of-field: A new method for the fusion of multichannel microscopy images

Microscopy imaging often suffers from limited depth-of-field. However, the specimen can be "optically sectioned" by moving the object along the optical axis. Then different areas appear in focus in different images. Extended depth-of-field is a fusion algorithm that combines those images into one single sharp composite. One promising method is based on the wavelet transform. Here, we show how the wavelet-based image fusion technique can be improved and easily extended to multichannel data. First, we propose the use of complex-valued wavelet bases, which seem to outperform traditional real-valued wavelet transforms. Second, we introduce a way to apply this technique for multichannel images that suppresses artifacts and does not introduce false colors, an important requirement for multichannel optical microscopy imaging. We evaluate our method on simulated image stacks and give results relevant to biological imaging.