Constrained least-squares restoration of nuclear medicine images: selecting the coarseness function

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.