We propose an offset-sparsity decomposition method for the enhancement of a color microscopic image of a stained specimen. The method decomposes vectorized spectral images into offset terms and sparse terms. A sparse term represents an enhanced image, and an offset term represents a "shadow." The related optimization problem is solved by computational improvement of the accelerated proximal gradient method used initially to solve the related rank-sparsity decomposition problem. Removal of an image-adapted color offset yields an enhanced image with improved colorimetric differences among the histological structures. This is verified by a no-reference colorfulness measure estimated from 35 specimens of the human liver, 1 specimen of the mouse liver stained with hematoxylin and eosin, 6 specimens of the mouse liver stained with Sudan III, and 3 specimens of the human liver stained with the anti-CD34 monoclonal antibody. The colorimetric difference improves on average by 43.86% with a 99% confidence interval (CI) of [35.35%, 51.62%]. Furthermore, according to the mean opinion score, estimated on the basis of the evaluations of five pathologists, images enhanced by the proposed method exhibit an average quality improvement of 16.60% with a 99% CI of [10.46%, 22.73%].