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This paper introduces a new feature-extraction-receiver-operating-characteristic (FEROC) test to evaluate the ability of image processing to improve the accuracy of the diagnostic information extracted from medical images. The test is applied to simulated planar nuclear images processed by the Pixon minimum-complexity method, originally developed in astronomy, which adaptively smoothes the images to bring out subtle contrasts with minimal loss of resolution. In addition, the processed images are fused with the raw counts with varying blending ratios to allow the readers to detect features with low signal-to-noise ratio, which the Pixon processor might smooth over because of their low statistical significance. The major conclusions from the study are: (1) Pixon processing can substantially increase the negative predictive value (specificity), i.e., reduce the false-positive rate, (2) the positive predictive value (sensitivity) increases modestly due to processing for Pixon blending <50% but declines to ~70% for higher blending percentages (unless it was already below 70% for the raw counts, in which case it is unaffected), (3) the improvement in the negative predictive value is most significant for count levels at which it is already ~80-90% for the raw counts (typical of clinical values), and (4) the improvement is less significant at lower counts (for which the negative predictive value is usually below clinical values) or higher counts (where there is not much to improve).