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.

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.

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.

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.

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.