Modifying constrained least-squares restoration for application to single photon emission computed tomography projection images
Penney, B C; King, M A; Schwinger, R B; Baker, S P; Doherty, P W
Image restoration methods have been shown to increase the contrast of nuclear medicine images by decreasing the effects of scatter and septal penetration. Image restoration can also reduce the high-frequency noise in the image. This study applies constrained least-squares (CLS) restoration to the projection images of single photon emission computed tomography (SPECT). In a previous study, it was noted that CLS restoration has the potential advantage of automatically adapting to the blurred object. This potential is confirmed using planar images. CLS restoration is then modified to improve its performance when applied to SPECT projection image sets. The modification was necessary because the Poisson noise in low count SPECT images causes considerable variation in the CLS filter. On phantom studies, count-dependent Metz restoration was slightly better than the modified CLS restoration method, according to measures of contrast and noise. However, CLS restoration was generally judged as yielding the best results when applied to clinical studies, apparently because of its ability to adapt to the image being restored.
Stationary and nonstationary spatial domain Metz filtering
King, M A; Miller, T R; Doherty, P W; Schwinger, R B
Stationary and nonstationary finite-impulse-response (FIR) implementations of the count-dependent Metz filter were investigated in this study. Filter size was observed to be an important variable controlling image quality. For Metz filtering of 128 X 128 pixel images at least a 15 X 15 term FIR filter was deemed necessary. By using an algorithm which selected between a set of preformed FIR filters based on pixel count, a nonstationary FIR implementation of the Metz filter was developed which required very little increase in execution time to stationary filtering. In a limited comparison of 'tumor' detection with stationary and nonstationary FIR filtering all of the Metz filtering techniques showed a significant improvement in detection when compared to the unprocessed images. However, no significant difference was observed between the stationary and nonstationary Metz filtering techniques. Thus, for Metz filters optimized solely on the basis of count, nonstationary FIR filtering does not seem to offer an advantage when compared to stationary filtering.
Constrained least-squares restoration of nuclear medicine images: selecting the coarseness function
Penney, B C; King, M A; Schwinger, R B; Baker, S P; Stritzke, P; Doherty, P W
Image restoration using the constrained least-squares (CLS) method theoretically adapts to the image being processed. In addition, it only requires knowing the modulation transfer function of the imaging system when applied to nuclear medicine images. Prompted by these observations, a systematic evaluation of the effects of the form of the "coarseness function" [C(f)] used by the CLS method has been conducted. Nine C(f)'s are evaluated using an observer preference and a normalized mean-squared error (NMSE) criterion. This evaluation is conducted for three modulation transfer functions and a wide range of count levels. The results of the subjective studies support using the form of C(f) which has been most widely employed in previous studies, i.e., the form designed to minimize the energy in the second derivative of the restored image. A different form of C(f) is generally found to be optimal by the mean-squared error criterion. The CLS method is then compared to: (1) no processing, (2) count-dependent smoothing, and (3) count-dependent Metz restoration. When evaluated using objective measurements of error and contrast, the CLS method is found to be slightly inferior to the best method, Metz restoration. However, CLS restoration is found to be equal to or better than the other methods when judged by the results of observer preference studies.
Interactive visual optimization of SPECT prereconstruction filtering
King, M A; Glick, S J; Penney, B C; Schwinger, R B; Doherty, P W
A number of factors must be considered when forming a digital filter to two-dimensionally filter single photon emission computed tomographic (SPECT) acquisition images. In an effort to provide subjectively optimal filtering, a program has been developed which provides "real-time" visual feedback. This allows a user to select from among a family of Metz filters tailored for the imaging conditions (i.e., formed to deconvolve scatter, septal penetration, and combined collimator and intrinsic spatial resolution losses). Also, a guideline for assisting the user in selecting from among the possible Metz filters has been formulated. This guideline is based upon knowledge of the probability distribution of the noise power spectrum, and consists of choosing the filter which has a value of 1.0 when the one-dimensional compression of the image power spectrum equals the 90% confidence limit for noise fluctuations. The program starts by filtering a planar reference image with the Metz filter computed for the radionuclide, collimator, magnification, and count-level of the image. This filter is displayed beside the image where it is overlayed on a plot of the logarithm of the one-dimensional compression of the image power spectrum. The user is then allowed to vary the filter parameters through movement of a joystick. By doing the filtering using an array processor, a new filtered image is formed and displayed less than a second after movement of the joystick. Visual feedback from the series of filtered images thus produced as well as the plots of the filter overlayed on the estimated blurred object power spectrum are used to obtain a visually "optimal" filter. The filter can be adapted to the visual preferences of the individual reader, and serves as a useful teaching tool on the effects of filtering.
Digital restoration of indium-111 and iodine-123 SPECT images with optimized Metz filters
King, M A; Schwinger, R B; Penney, B C; Doherty, P W; Bianco, J A
A number of radiopharmaceuticals of great current clinical interest for imaging are labeled with radionuclides that emit medium- to high-energy photons either as their primary radiation, or in low abundance in addition to their primary radiation. The imaging characteristics of these radionuclides result in gamma camera image quality that is inferior to that of 99mTc images. Thus, in this investigation 111In and 123I contaminated with approximately 4% 124I were chosen to test the hypothesis that a dramatic improvement in planar and SPECT images may be obtainable with digital image restoration. The count-dependent Metz filter is shown to be able to deconvolve the rapid drop at low spatial frequencies in the imaging system modulation transfer function (MTF) resulting from the acceptance of septal penetration and scatter in the camera window. Use of the Metz filter was found to result in improved spatial resolution as measured by both the full width at half maximum and full width at tenth maximum for both planar and SPECT studies. Two-dimensional, prereconstruction filtering with optimized Metz filters was also determined to improve image contrast, while decreasing the noise level for SPECT studies. A dramatic improvement in image quality was observed with the clinical application of this filter to SPECT imaging.
Area weighted convolutional interpolation for data reprojection in single photon emission computed tomography
Schwinger, R B; Cool, S L; King, M A
A data reprojection algorithm has been developed for use in single photon emission computed tomography on an array processor equipped computer system. The algorithm makes use of an accurate representation of pixel activity (uniform square pixel model of intensity distribution), and is rapidly performed due to the efficient handling of an array-based algorithm and the fast Fourier transform on parallel processing hardware. The algorithm consists of using a pixel driven nearest-neighbor projection operation to an array of subdivided projection bins. The subdivided project bin array is then convolved with the angle-dependent projection of the area of a uniform square pixel and compressed to original bin size. The new algorithm has thus been named the area weighted convolution (AWC) method of interpolation. When compared to nearest-neighbor and linear interpolation algorithms, the new AWC algorithm was found to be more accurate, having an accuracy approaching that of the line length algorithm. It also yielded an easier and more efficient implementation on parallel hardware than line length or linear interpolation, with faster execution times than either.
Variation of the count-dependent Metz filter with imaging system modulation transfer function
King, M A; Schwinger, R B; Penney, B C
A systematic investigation was conducted of how a number of parameters which alter the system modulation transfer function (MTF) influence the count-dependent Metz filter. Since restoration filters are most effective at those frequencies where the object power spectrum dominates that of the noise, it was observed that parameters which significantly degrade the MTF at low spatial frequencies strongly influence the formation of the Metz filter. Thus the radionuclide imaged and the depth of the source in a scattering medium had the most influence. This is because they alter the relative amount of scattered radiation being imaged. For low-energy photon emitters, the collimator employed and the distance from the collimator were found to have less of an influence but still to be significant. These cause alterations in the MTF which are more gradual, and hence are most pronounced at mid to high spatial frequencies. As long as adequate spatial sampling is employed, the Metz filter was determined to be independent of the exact size of the sampling bin width, to a first approximation. For planar and single photon emission computed tomographic (SPECT) imaging, it is shown that two-dimensional filtering with the Metz filter optimized for the imaging conditions is able to deconvolve scatter and other causes of spatial resolution loss while diminishing noise, all in a balanced manner.
Two-dimensional filtering of SPECT images using the Metz and Wiener filters
King, M A; Schwinger, R B; Doherty, P W; Penney, B C
Two-dimensional filtering, both before and after reconstruction, has been applied to the processing of single photon emission computerized tomographic (SPECT) images. The filters investigated were the count-dependent Metz filter and Wiener filter, both of which automatically adapt to the image being processed. Using a SPECT phantom, with images reconstructed with these filters rather than the ramp, we observed a statistically significant increase (p less than 0.05) in the image contrast for solid Plexiglas spheres, and significant decrease (p less than 0.05) in the percent fractional standard deviation of counts in a region of uniform activity. The adaptability of these filters is demonstrated by a comparison of SPECT acquisitions of the phantom at two different count levels. An example of their application to clinical studies is presented. We conclude that two-dimensional digital image restoration with these techniques can produce a significant increase in SPECT image quality, with a small cost in processing time when these techniques are implemented on an array processor.
A Wiener filter for nuclear medicine images
King, M A; Doherty, P W; Schwinger, R B; Penney, B C
To improve the quality of digital nuclear medicine images, we have developed a new implementation of the Wiener restoration filter. The Wiener filter uses as its optimality criterion the minimization of the mean-square error between the undistorted image of the object and the filtered image. In order to form this filter, the object and noise power spectrums are needed. The noise power spectrum for the count-dependent Poisson noise of nuclear medicine images is shown to have a constant average magnitude equal to the total count in the image. The object power spectrum is taken to be the image power spectrum minus the total count, except in the noise dominated region of the image power spectrum where a least-squares-fitted exponential is used. Processing time is kept to a clinically acceptable time frame through use of an array processor. Pronounced noise suppression and detail enhancement are noted with use of this filter with clinical images.
Fast count-dependent digital filtering of nuclear medicine images: concise communication
King, M A; Doherty, P W; Schwinger, R B; Jacobs, D A; Kidder, R E; Miller, T R
The formulation of an "optimal" filter for improving the quality of digitally recorded nuclear medicine images is reported in this paper. The method forms a Metz filter for each image based upon the total number of counts in the image, which in turn determines the average noise level. The parameters of the filter were optimized for a set of simulated images using the minimization of the mean-square error as the criterion. The speed of the image formation results from the use of an array processor. In a study of localization receiver operating characteristics (LROC) using the Alderson liver phantom, a significant improvement in tumor localization was found in images filtered with this technique, compared with the original digital images and those filtered by the nine-point binomial smoothing algorithm. The technique has been found useful for the filtering of static and dynamic studies as well as the two-dimensional pre-reconstruction filtering of images from single photon emission computerized tomography.