A Wiener filter for nuclear medicine images

Vertebral and ribs enhancement in Tc-99m methylene diphosphonate bone scan image by blind deconvolution algorithm

AIMS AND OBJECTIVES

The objective of the study was to restore Tc-99m methylene diphosphonate (MDP) bone scan image using blind deconvolution (BD) algorithm so that ribs, vertebrae, and lesions present in them become prominent.

MATERIALS AND METHODS

Our study consists of retrospective data in which 356 Tc-99m MDP bone scan images (178 anterior and 178 posterior) were processed using dynamic stochastic resonance algorithm, block-matching 3D filter, and then restored using BD algorithm. Two nuclear medicine (NM) physicians compared restored image with its input image; they especially lookedfor: (a) improvement in lesions detectability, (b) artifacts if any, (c) deterioration in ribs and vertebra, and (d) contrast enhancement in adjacent vertebra and adjacent ribs. They selected one out of two (restored and input) images, which had better quality. The overall image quality was also assessed using the following image quality metrics: brightness, blur, global contrast factor, and contrast per pixel. The Wilcoxon signed-rank test was applied for finding significant difference between the value of image quality metrics of restored image and input image at level of significance alpha = 0.05.

RESULTS

According to NM physicians, 80.3% (286 out of 356) of restored images were acceptable, whereas 19.6% (70 out of 356) were unacceptable. Ribs and vertebrae were prominent in 161 out of 178 posterior restored images. Lumbar vertebrae were enhanced and well differentiated from adjacent vertebrae in 125 out of 178 anterior restored images. The value of image quality metrics of restored and input images were found to be significantly different ( P -value < 0.0001).

CONCLUSION

Ribs, vertebrae, and lesions present in them become prominent in the most of Tc-99m MDP bone scan images (80.3%) restored using BD algorithm.

Restoration of Tc-99m methyl diphosphonate bone scan image using Richardson-Lucy algorithm

INTRODUCTION

In this study, the optimal input parameters point spread function (PSF) and the number of iterations of the Richardson-Lucy algorithm were experimentally determined to restore Tc-99 m methyl diphosphonate (MDP) whole-body bone scan images.

MATERIALS AND METHODS

The experiment was performed on 60 anonymized Tc-99 m MDP whole-body bone scan images. Ten images were used for estimating the optimum value of PSF and the number of iterations to restore scintigraphic images. The remaining 50 images were used for validation of estimated parameters. The image quality of observed and restored images was assessed objectively using blind/referenceless image spatial quality evaluator (BRISQUE), mean brightness (MB), discrete entropy (DE), and edge-based contrast measure (EBCM) image quality metrics. Image quality was subjectively assessed by two nuclear medicine physicians (NMPs) by comparing the restored image quality with observed image quality and assigning a score to each image on the scale of 0-5.

RESULTS

Based on BRISQUE, MB, DE, and EBCM scores, the restored images were significantly sharper, less bright, had more detailed information, and had less contrast around edges compared to the input images. The restored images had improved resolution based on visual assessment as well; NMPs assigned an average image quality score of 4.00 to restored images. Maximum resolution enhancement was noticed at PSF (size: 11 pixels, sigma: 1.75 pixels) and the number of iterations = 10. With the increase in the number of iterations, noise also gets amplified along with resolution enhancement and affects the detectability of small lesions; in the case of relatively low noisy input images, the number of iterations = 5 gave better results.

CONCLUSION

Tc-99 m MDP bone scan images were restored to improve image quality using the Richardson-Lucy algorithm. The optimum value of the PSF parameter was found to be of size = 11 pixels and sigma = 1.75 pixels.

Restoration of I-131 whole body image using a Wiener filter

INTRODUCTION

The aim of the study was to restore I-131 whole body image using Wiener filter.

MATERIAL AND METHODS

A set of 50 I-131 whole body images acquired using Symbia E dual head gamma camera with high energy general purpose collimator was used. The Gaussian point-spread function (PSF) characterised by the size (3, 5, 7, 9, 11, and 13 pixels) and corresponding standard deviation (0.5, 0.75, 1, 1.5, 1.75, and 2 pixels) and noise-to-signal power ratios (NSR: 0, 0.001, 0.01, 0.1, 0.2, 0.3, 0.4, and 0.5) were used as parameters for Wiener filter. Using the combinations of PSF and NSR, a total of 2450 images (50 × 49 = 2450 images, where 49 images include 1 input and 48 restored images for each input image) were generated and inspected by two nuclear medicine physicians. They selected one best image (the image which had less noise and better contrast between the lesion and background in comparison with the input image). Their results were analyzed.

RESULTS

Compared to input image, the metastatic uptake in restored images was very easily perceived. The restored image obtained with PSF (size = 13, sigma = 2) and NSR = 0.3 had better signal-to-noise ratio in comparison to restored image obtained with PSF (size = 11, sigma = 1.75) and NSR = 0.2.

CONCLUSION

The restored images with PSF (size = 13, sigma = 2) and NSR = 0.3 were found to have superior image quality in comparison with its input image.

Denoising of iodine-131 images using a median filter

OBJECTIVE

An iodine-131 (I) image visually appears to be contaminated with impulse noise. The two-dimensional median filter removes noise without sacrificing the edge information. Its performance depends on the shape and size of the mask. In this study, we have compared the performance of a plus-shape and a square-shape median filter for I whole-body images and found the filter with optimum parameter that improves I image quality acceptable to nuclear medicine physicians.

MATERIALS AND METHODS

A total of 150 whole-body I images were exported in DICOM format. These images were converted into PNG format and processed with a plus-shape and a square-shape median filter, with each shape mask having sizes of 3, 5, 7, and 9 pixels. The quality of the processed images was assessed by visual assessment by two nuclear medicine physicians and also quantitatively by evaluating metrics: mutual information, mean square error, peak signal-to-noise ratio, and difference entropy. Nuclear medicine physicians assigned a score to each image on the scale 1 (lowest) to 5 (highest) for image quality on the basis of the noise removal, smoothness, and edge information available in the image. Student's t-test was carried out to find the significant difference in the image quality (α=0.05) between the processed images with square-shape and cross-shape mask with the same pixel size. All experiments including statistical analysis were conducted using R installed on a personal computer.

RESULTS

Both median filters improved the image quality of I images. The plus-shape median filter was found to show better performance in comparison with the square-shape median filter (P<0.001). The plus-shape median filter with a mask size of 7 pixels was found to be optimum for the processing of whole-body I images.

CONCLUSION

The plus-shape median filter with a mask size of 7 pixels can be used to process whole-body I scintigraphic images without loss of clinical information.

Nonlinear spatio-temporal filtering of dynamic PET data using a four-dimensional Gaussian filter and expectation-maximization deconvolution

We introduce a method for denoising dynamic PET data, spatio-temporal expectation-maximization (STEM) filtering, that combines four-dimensional Gaussian filtering withEMdeconvolution. The initial Gaussian filter suppresses noise at a broad range of spatial and temporal frequencies and EM deconvolution quickly restores the frequencies most important to the signal. We aim to demonstrate that STEM filtering can improve variance in both individual time frames and in parametric images without introducing significant bias. We evaluate STEM filtering with a dynamic phantom study, and with simulated and human dynamic PET studies of a tracer with reversible binding behaviour, [C-11]raclopride, and a tracer with irreversible binding behaviour, [F-18]FDOPA. STEM filtering is compared to a number of established three and four-dimensional denoising methods. STEM filtering provides substantial improvements in variance in both individual time frames and in parametric images generated with a number of kinetic analysis techniques while introducing little bias. STEM filtering does bias early frames, but this does not affect quantitative parameter estimates. STEM filtering is shown to be superior to the other simple denoising methods studied. STEM filtering is a simple and effective denoising method that could be valuable for a wide range of dynamic PET applications.

Adaptive noise reduction of scintigrams with a wavelet transform

The aim of this study was to eliminate the effect of Poisson noise in scintigrams with a wavelet thresholding method. We developed a new noise reduction method with a wavelet transform. The proposed method was a combination of the translation-invariant denoising method and our newly introduced denoising filter which was applicable for Poisson noise. To evaluate the validity of our proposed method, phantom images and scintigrams were used. The results with the phantom images showed that our method was better than conventional methods in terms of the peak signal-to-noise ratio by 3 dB. Quality of the scintigrams processed with our method was better than that with the conventional methods in terms of reducing Poisson noise while preserving edge components. The results demonstrated that the proposed method was effective for the reduction of Poisson noise in scintigrams.

Resolution improvement in emission optical projection tomography

A new imaging technique called emission optical projection tomography (eOPT), essentially an optical version of single-photon emission computed tomography (SPECT), provides molecular specificity, resolution on the order of microns to tens of microns, and large specimen coverage ( approximately 1 cubic centimetre). It is ideally suited to gene expression studies in embryos. Reconstructed eOPT images suffer from blurring that worsens as the distance from the axis of rotation increases. This blur is caused in part by the defocusing of the lens' point-spread function, which increases with object distance from the focal plane. In this paper, we describe a frequency space filter based on the frequency-distance relationship of sinograms to deconvolve the distance-dependent point-spread function and exclude highly defocused data from the eOPT sinograms prior to reconstruction. The method is shown to reduce the volume at half-maximum of the reconstructed point-spread function to approximately 20% the original, and the volume at 10% maximum to approximately 6% the original. As an illustration, the visibility of fine details in the vasculature of a 9.5 day old mouse embryo is dramatically improved.

Development of a collimator blurring compensation method using fine angular sampling projection data in SPECT

Due to the collimator aperture, spatial resolution of SPECT data varies with source-to-detector distance. Since the radius of detector rotation is bigger when scanning larger patients, spatial resolution is degraded in these cases. Emitted gamma rays travel not only along the central axis of the collimator hole but also off-axis due to the collimator aperture. However, an off-axis ray at one angle would be a central-axis ray at another angle; therefore, raw projection data at one angle can be thought of as an ensemble of central-axis rays collected from a small arc equal to the collimator aperture. Thus, fine angular sampling can compensate for collimator blurring. By using a sampling pitch of less than half the collimator aperture angle, compensation was performed by subtracting the weighted sum of the projection data from the raw projection data. Collimator geometry and detector rotation radius determined the weighting function. Cylindrical phantom with four different-sized rods and torso phantom for Tl-201 cardiac SPECT simulation were used for evaluation. Aperture angle of the collimator was 7 degrees. Projection sampling pitch was 2 degrees. In both phantom studies, the proposed method showed improvement in contrast and reduction of partial volume effect, thereby indicating that the proposed method can compensate adequately for image blurring caused by the collimator aperture.

Improved lesion detection from spatially adaptive, minimally complex, Pixon® reconstruction of planar scintigraphic images

Pixon noise reduction was applied to 18 planar images, six each from 99mTc-methylene diphosphonate (99mTc-MDP), 67Ga citrate (67Ga), and (123)I-metaiodobenzylguanidine ((123)I-MIBG) studies. Pixon processing increased patient signal-to-noise ratio, 6.8-11.8 fold. Three specialists preferred processed images 44 of 54 times with good agreement (87%). Most (9/10, p<0.02) of the null and negative preferences were from (123)I-MIBG studies. Inter-rater association was shown for 1-4 scale rated artifact p<0.1, noise p<0.01 and lesion detection p<0.05. Pixon images had superior lesion detection ability, p<0.02, and noise levels, p<0.02 and no statistically significant change in artifacts.

A linear wavelet filter for parametric imaging with dynamic PET

This paper describes a new filter for parametric images obtained from dynamic positron emission tomography (PET) studies. The filter is based on the wavelet transform following the heuristics of a previously published method that are here developed into a rigorous theoretical framework. It is shown that the space-time problem of modeling a dynamic PET sequence reduces to the classical one of estimation of a normal multivariate vector of independent wavelet coefficients that, under least-squares risk, can be solved by straightforward application of well established theory. From the study of the distribution of wavelet coefficients of PET images, it is inferred that a James-Stein linear estimator is more suitable for the problem than traditional nonlinear procedures that are incorporated in standard wavelet filters. This is confirmed by the superior performance of the James-Stein filter in simulation studies compared to a state-of-the-art nonlinear wavelet filter and a nonstationary filter selected from literature. Finally, the formal framework is interpreted for the practitioner's point of view and advantages and limitations of the method are discussed.

Resolution recovery for list-mode reconstruction in SPECT

The purpose of the study was to evaluate the resolution recovery in the list-mode iterative reconstruction algorithm (LMIRA) for SPECT. In this study we compare the performance of the proposed method with other iterative resolution recovery methods for different noise levels. We developed an iterative reconstruction method which uses list-mode data instead of binned data. The new algorithm makes use of a more accurate model of the collimator structure. We compared the SPECT list-mode reconstruction with MLEM, OSEM and RBI, all including resolution recovery. For the evaluation we used Gaussian shaped sources with different FWHM at three different locations and three noise levels. For these distributions we calculated the reconstructed images for a different number of iterations. The absolute error for the reconstructed images was used to evaluate the performance. The performance of all four methods is comparable for the sources located in the centre of the field of view. For the sources located out of the centre, the error of the list-mode method is significantly lower than that of the other methods. Splitting the system model into a separate object-dependent and detector-dependent module gives us a flexible reconstruction method. With this we can very easily adapt the resolution recovery to different collimator types.

Noise and signal decoupling in maximum-likelihood reconstructions and Metz filters for PET brain images

Images reconstructed with the maximum-likelihood-by-expectation-maximization (ML) algorithm have lower noise in some regions, particularly low count areas, compared with images reconstructed with filtered backprojection (FBP). The use of statistically correct noise model coupled with the positivity constraint in the ML algorithm provides this noise improvement, but whether this model confers a general advantage for ML over FBP with no noise model and any reconstruction filter, is unclear. We have studied the quantitative impact of the correct noise model in the ML algorithm applied to simulated and real PET fluoro-deoxyglucose (FDG) brain images, given a simplified but accurate reconstruction model with spatially invariant resolution. For FBP reconstruction, several Metz filters were chosen and images with different resolution were obtained depending on the order (1-400) of the Metz filters. Comparisons were made based on the mean Fourier spectra of the projection amplitudes, the noise-power spectra, and the mean region-of-interest signal and noise behaviour in the images. For images with resolution recovery beyond the intrinsic detector resolution, the noise increased significantly for FBP compared with ML. This indicates that in the process of signal recovery using ML, the noise is decoupled from the signal. Such noise decoupling is not possible for FBP. However, for image resolution equivalent to or less than the intrinsic detector resolution, FBP with Metz filters of various orders can achieve a performance similar to ML. The significance of the noise decoupling advantage in ML is dependent on the reconstructed image resolution required for specific imaging tasks.

Quantitative cardiac SPECT in three dimensions: validation by experimental phantom studies

A mathematical framework for quantitative SPECT (single photon emission computed tomography) reconstruction of the heart is presented. An efficient simultaneous compensation approach to the reconstruction task is described. The implementation of the approach on a digital computer is delineated. The approach was validated by experimental data acquired from chest phantoms. The phantoms consisted of a cylindrical elliptical tank of Plexiglass, a cardiac insert made of Plexiglass, a spine insert of packed bone meal and lung inserts made of styrofoam beads alone. Water bags were added to simulate different body characteristics. Comparison between the quantitative reconstruction and the conventional FBP (filtered backprojection) method was performed. The FBP reconstruction had a poor quantitative accuracy and varied for different body configurations. Significant improvement in reconstruction accuracy by the quantitative approach was demonstrated with a moderate computing time on a currently available desktop computer. Furthermore, the quantitative reconstruction was robust for different body characteristics. Therefore, the quantitative approach has the potential for clinical use.

The determination of the effective attenuation coefficient from effective organ depth and modulation transfer function in gamma camera imaging

Absolute measurement of activity implies a determination of effective depths and effective attenuation coefficients. In order to define restoration filters, it is necessary to measure the transfer function, i.e. position a line source at an effective depth for the specific measurement situation. A phantom was designed which can simulate an organ with a certain thickness at a certain depth. The phantom was used to measure transfer functions and a comparison was made with transfer functions from a line source to determine effective depths. Effective attenuation coefficients were calculated for 99mTc, 111In and 201Tl for different organ thicknesses and depths of simulated organs. The effective attenuation coefficient for 99mTc was found to be 0.124 +/- 0.006 cm-1, in good agreement with previously published values. For 111In, the attenuation coefficient decreased with the depth of an organ due to the use of two energy windows in the measurements and a corresponding change in mean photon energy by depth. For 201Tl, the attenuation coefficient decreased with increasing organ thickness due to the increasing fraction of scattered radiation in the 40% energy window used. Using attenuation coefficients of 0.124, 0.184 and 0.11 cm-1 for 99mTc, 201Tl and 111In respectively, the derived equations can be used to calculate the position of a conventional line source for measurements of transfer functions for a specific organ with a certain thickness at a certain depth for definition of different types of restoration filter.

Stimulating technetium-99m cerebral perfusion studies with a three-dimensional Hoffmann brain phantom: collimator and filter selection in SPECT neuroimaging

The choice of collimator and the selection of a filter can affect the quality of clinical SPECT images of the brain. The compromises that 4 different collimators make between spatial resolution and sensitivity were studied by imaging a three-dimensional Hoffmann brain phantom. The planar data were acquired with each collimator on a three-headed SPECT system and were reconstructed with both a standard Butterworth filter and a Wiener pre-filter. The reconstructed images were then evaluated by specialists in nuclear medicine and were also quantitatively analyzed with specific regions of interest (ROI) in the brain. All observers preferred the Wiener filter reconstructed images regardless of the collimator used to acquire the planar images. With this filter, the ultrahigh-resolution fan-beam collimator was the most subjectively preferable and quantitatively produced the highest contrast ratios. The findings support suggestions that higher resolution collimators are preferable to higher sensitivity collimators, and indicate that fan-beam collimators are preferable to parallel-hole collimators for clinical SPECT studies of cerebral perfusion. The results also suggest that Wiener filter enhances the quality of SPECT brain images regardless of which collimator is used to acquire the data.

Iterative correction method for shift-variant blurring caused by collimator aperture in SPECT

A collimation system in single photon computed tomography (SPECT) induces blurring on reconstructed images. The blurring varies with the collimator aperture which is determined by the shape of the hole (its diameter and length), and with the distance between the collimator surface and the object. The blurring has shift-variant properties. This paper presents a new iterative method for correcting the shift-variant blurring. The method estimates the ratio of "ideal projection value" to "measured projection value" at each sample point. The term "ideal projection value" means the number of photons which enter the hole perpendicular to the collimator surface, and the term "measured projection value" means the number of photons which enter the hole at acute angles to the collimator aperture axis. If the estimation is accurate, ideal projection value can be obtained as the product of the measured projection value and the estimated ratio. The accuracy of the estimation is improved iteratively by comparing the measured projection vale with a weighted summation of several estimated projection value. The simulation results showed spatial resolution was improved without amplification of artifacts due to statistical noise.

A vector Wiener filter for dual-radionuclide imaging

The routine use of a single radionuclide for patient imaging in nuclear medicine can be complemented by studies employing two tracers to examine two different processes in a single organ, most frequently by simultaneous imaging of both radionuclides in two different energy windows. In addition, simultaneous transmission/emission imaging with dual-radionuclides has been described, with one radionuclide used for the transmission study and a second for the emission study. There is thus currently considerable interest in dual-radionuclide imaging. A major problem with all dual-radionuclide imaging is the "crosstalk" between the two radionuclides. Such crosstalk frequently occurs, because scattered radiation from the higher energy radionuclide is detected in the lower energy window, and because the lower energy radionuclide may have higher energy emissions which are detected in the higher energy window. The authors have previously described the use of Fourier-based restoration filtering in single photon emission computed tomography (SPECT) and positron emission tomography (PET) to improve quantitative accuracy by designing a Wiener or other Fourier filter to partially restore the loss of contrast due to scatter and finite spatial resolution effects. The authors describe here the derivation and initial validation of an extension of such filtering for dual-radionuclide imaging that simultaneously 1) improves contrast in each radionuclide's "direct" image, 2) reduces image noise, and 3) reduces the crosstalk contribution from the other radionuclide. This filter is based on a vector version of the Wiener filter, which is shown to be superior [in the minimum mean square error (MMSE) sense] to the sequential application of separate crosstalk and restoration filters.

Computation of left ventricular volume curves from gated blood pool studies without explicit use of edge detection algorithms: concise communication

A new technique has been developed to compute left ventricular (LV) time activity curves from gated blood pool (GBP) studies without the use of manual, semiautomated or fully automated edge detection algorithms. The method utilizes the correlation of entropy calculated from the counts of a fixed region of interest covering the left ventricle during a cardiac cycle to compute the LV volume curve for a new patient. The new LV volume curve is obtained through interpolation of those volume curves of a data base which are associated with the closest variations in normalized entropy to the new one. The computed LV time activity curves agree with those obtained from manual or fully automated outlines of the left ventricle within 9 percent for the selected set of 67 patients demonstrating the potential of the method. The accuracy of calculated LV volume curves can be improved theoretically to any degree by increasing the number of cases in the data base of known statistical feature vectors associated with the LV images and LV volume curves. The new method for computation of LV curves is very efficient and robust when compared to traditional techniques.

Fourier correction for spatially variant collimator blurring in SPECT

In single-photon emission computed tomography (SPECT), projection data are acquired by rotating the photon detector around a patient, either in a circular orbit or in a noncircular orbit. The projection data of the desired spatial distribution of emission activity is blurred by the point-response function of the collimator that is used to define the range of directions of gamma-ray photons reaching the detector. The point-response function of the collimator is not spatially stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual distance-dependent point-response function by a spatially invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. A method is described here for distance-dependent preprocessing of SPECT projection data prior to image reconstruction. Based on the special distance-dependent characteristics of the Fourier coefficients of the sinogram, a spatially variant inverse filter can be developed to process the projection data in all views simultaneously. The algorithm is first derived from Fourier analysis of the projection data from the circular orbit geometry. For circular orbit projection data, experimental results from both simulated data and real phantom data indicate the potential of this method. It is shown that the spatial filtering method can be extended to the projection data from the noncircular orbit geometry. Experiments on simulated projection data from an elliptical orbit demonstrate correction of the spatially variant blurring and distortion in the reconstructed image caused by the noncircular orbit geometry.

Deconvolution of planar scintigrams by maximum entropy

Planar scintigrams are deconvolved with a point spread function using the maximum entropy method with the aim of improving image quality. The technique requires the specification of several parameters. These are related to the level of noise present in the data and our a priori knowledge of the object imaged. The performance of the technique is tested for a wide range of these parameters using images of a Williams phantom in scattering material and a figure of merit, derived from the detectability of the smallest cold spot, is calculated. For close to optimal values of the parameters a factor of two improvement in the figure is found. A processed bone image shows improved contrast and resolution. Maximum entropy processing could be used to increase image quality or allow comparable image quality with reduced imaging time or patient dose.

Predictor-corrector with cubic spline method for spectrum estimation in Compton scatter correction of SPECT

In single photon emission computed tomography (SPECT), Compton scattered photons degrade image contrast and cause erroneous regional activity quantification. A predictor-corrector and cubic spline (PCCS) method for the compensation of Compton scatter in SPECT is proposed. Using spectral information recorded at four energy windows, the PCCS method estimates scatter counts at each window and constructs the scatter spectrum with cubic spline interpolation. We have shown in simulated noise-free situations that this method provides accurate estimation of scatter fractions. A scatter correction employing PCCS method can be implemented on many existing SPECT systems without hardware modification and complicated calibration.

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.

Using mathematical morphology to determine left ventricular contours

The aim of this study is to investigate the use of mathematical morphology for the determination of left ventricular contours in scintigraphic images using multigated radionuclide angiography. We have developed a completely automatic method that first restores the image with a Wiener filter, then finds the region where the left ventricle is contained, and finally segments the left ventricle contour and a background zone. The contours depend on the values of the parameters that appear in the mathematical morphology method, which are related to the height and the slope of the count distribution. Results obtained with this method are compared with the contours and the background zones outlined by experts on the basis of the number of counts. We study the values of the parameters with which the optimum correlation is obtained.

Order statistic-neural network hybrid filters for gamma camera-bremsstrahlung image restoration

An order statistic and neural network hybrid filter (OSNNH) is proposed for the restoration of gamma camera images using the measured modulation transfer function. Planar images of beta-emitting radionuclides are used to evaluate the filter because they exhibit higher degradation than images of single photon emitters due to increased photon scattering and collimator septal penetration. The filter performance is quantitatively evaluated and compared to that of the Wiener filter by investigating the relationship between the externally measured counts from sources of phosphorous-32 ((32)P) at various depths in water. An effective linear attenuation coefficient for (32)P is determined to be equal to 0.13 cm(-1) and 0.14 cm(-1) for the OSNNH and the Wiener filters, respectively. Evaluation of phantom and patient filtered images demonstrates that the OSNNH filter avoids ring effects caused by the ill-conditioned blur matrix and noise overriding caused by matrix inversion, typical of other restoration filters such as the Wiener.

Improved positron emission tomography quantification by Fourier-based restoration filtering

Positron emission tomography (PET) images are characterized by both poor spatial resolution and high statistical noise. Conventional methods to reduce noise, such as local weighted averaging, produce further deteriorations in spatial resolution, while the use of deconvolution to recover resolution typically amplifies noise to unacceptable levels. We studied the use of two-dimensional Fourier filtering to simultaneously increase quantitative recovery and reduce noise. The filter was based on inversion of the scanner's measured transfer function, coupled with high frequency roll-off. In phantom studies, we found improvements in both "hot" and "cold" sphere quantification. Compared with ramp-only filtering, improvements in hot spot recovery for the highest accuracy filter averaged 13.6% +/- 6.6% for spheres larger than 15 mm; improvements in cold spot recovery averaged 30.7% +/- 4.7%. At the same time, the noise was reduced by a factor of 3 compared with randomly filtering. Fourier-based image restoration filtering is thus capable of improving both accuracy and precision in PET.

Constrained least-squares restoration and renogram deconvolution: a comparison by simulation

Before deconvolution can be used in renography, it is necessary to decide whether the renal function is sufficiently good to allow it. To see if this decision can be circumvented, an iterative constrained least-squares restoration (CLSR) method was implemented in which the point of termination of the iteration occurs when a residual vector has a value less than an estimate of the noise in the original renogram curve. The technique was compared with the matrix algorithm and with direct FFT division. The comparison was achieved by deconvolving simulated renogram data with differing transit time spectra and statistics. As expected, the FFT technique produced results of little value whereas the CLSR and matrix methods produced values of mean transit time (MTT) that differed slightly from the expected results. Analysis indicated that the matrix approach was superior when the percentage noise component was less than 6% and vice versa. No technique produced useful transit time spectra. As the CLSR technique produced better results than the matrix method in simulations with relatively long MTTs and high noise, it seems reasonable to suggest that it might be used for renogram deconvolution without the need for previous inspection of the curves.

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.

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.

Non-stationary spatial filtering and accelerated curve fitting for parametric imaging with dynamic PET

A non-stationary spatial low pass filter was developed and implemented in combination with an accelerated non-linear curve fitting routine to create low noise-high contrast images of physiological parameters with dynamic positron emission tomography. The method was applied to 18F-2-fluoro-2-deoxyglucose (FDG) studies, and images of local blood volume, kinetic rate constants, precursor pool volume and glucose metabolism were generated. Noise reduction and contrast preservation was demonstrated in a simulated pie phantom and a study of a patient with a recent brain infarct. Considerably improvement in quantitative accuracy of pixel parameter values was observed in the phantom study in comparison with unprocessed or conventionally smoothed images.

Interactive digital filtering of gated cardiac studies during cine display

The use of a novel class of image processing hardware, the image computer, is illustrated by application to gated cardiac studies. Digital filtering of a nine-view study consisting of 144 frames, each 64x64 pixels in size, is performed using the Wiener filter. During image display the operator can change the filter parameters. Refiltering is then performed essentially instantaneously, permitting truly interactive filter selection. Comparable digital filtering using a fast conventional computer and display hardware is shown to be too slow to permit interactive filter modification. Image computers incorporate very large image memories with very tightly coupled, fast arithmetic processors and video display devices and allow very computation-intensive calculations to be performed interactively.

A comparison of deconvolution and windowed subtraction techniques for scatter compensation in SPECT

Three procedures for the removal of Compton-scattered data in SPECT by constrained deconvolution are presented. The first is a deconvolution of a 2-D measured PSRF containing scatter from a single reconstructed transaxial image; the second is a deconvolution of a 2-D measured point-source response function (PSRF) from each frame of projection data prior to reconstruction; the third involves deconvolution of a 3-D measured PSRF from a stack of reconstructed slices. Results of applying these procedures to data obtained from a phantom containing cold cylinders and to data from a cold spot-resolution phantom are presented and are shown to be superior to the results of correcting for scatter by scatter-window substraction. Both 3-D deconvolution from reconstructed images and 2-D deconvolution from projection data show major improvements in image contrast, resolution, and quantitation. Improvements are especially marked for small (1.0-3.0 cm) cold sources.

Digital restoration of scintigraphic images by a two-step procedure

A two-step procedure for restoring scintigraphic images is described. The first step uses a local-statistics algorithm for improvement in signal-to-noise ratio by smoothing the Poisson noise. The second step aims at improvement in spatial resolution by removing the linear blur using the iterative restoration algorithm. We present some results of computer simulations and restoration of scintigraphic images that demonstrate the effectiveness of the proposed procedure.

Functional image data acquisition and processing

In the production of functional images certain hardware and software considerations are necessary for the rapid and accurate determination of kinetic parameters. The advent of the digital scintillation camera has made available increased accuracy of quantitation and ease of image handling, although its integrated computer system may not be optimal for program development presently. To reduce the deleterious effects of Poisson noise on parameter estimation, the single or multiple application of easily implemented smoothing operators in space and time is recommended as a first step in image processing. The properties of these operators are conveniently expressed in terms of their variance. Following smoothing, count or variance thresholding is performed to reduce computer processing time and eliminate extraneous background from functional images. Time-activity curves can be fit by a variety of mathematical functions, the most useful of which is probably the finite Fourier series. In a simulated gated blood-pool study of the left ventricle, with and without an aneurysm, it is found that increased smoothing of the original image data results in more accurate parameter determinations, to the extent that small regions of dissimilar temporal behavior are not obliterated.

Improvement of Lesion Detection in Scintigraphic Images by SVD Techniques for Resolution Recovery

The properties of singular value decomposition (SVD) are used to implement an SVD spatial domain pseudoinverse restoration filter. This type of filter is attractive for poor imaging conditions (low spatial resolution, high image noise) and is thus appealing for nuclear medicine images. The method might offer some advantages over more traditional frequency domain filter techniques since the restoration is performed on a local rather than global basis. High-contrast thyroid phantom images collected at different count densities and low-contrast liver phantom images were processed with the SVD filter. Restored images yielded improved spatial resolution, lesion contrast, and signal-to-noise ratio. The SVD pseudoinverse restoration filter implemented as an interactive process permits the operator to terminate filtering at a stage where the visually "best" image is obtained compared to the original data. Processed images suggest that the technique may have potential for improving lesion detection in nuclear medicine.

Use of a nonstationary temporal Wiener filter in nuclear medicine

The use of the Wiener filter is proposed for temporal filtering of nuclear medicine dynamic studies. This filter adapts to the signal and noise levels of each pixel activity curve in a dynamic study to produce an "optimal" suppression of noise, while maintaining the signal content of the curve. The filter is derived to be a simple function of the power spectrum of the time-activity curve. Examples of its use for temporally filtering gated blood-pool studies for cine viewing and functional image formation are shown.