There has been a considerable interest in sparse representation and compressive sensing in applied mathematics and signal processing in recent years but with limited success to medical image processing. In this paper we developed a sparse representation-based classification (SRC) algorithm based on L1-norm minimization for classifying chromosomes from multicolor fluorescence in situ hybridization (M-FISH) images. The algorithm has been tested on a comprehensive M-FISH database that we established, demonstrating improved performance in classification. When compared with other pixel-wise M-FISH image classifiers such as fuzzy c-means (FCM) clustering algorithms and adaptive fuzzy c-means (AFCM) clustering algorithms that we proposed earlier the current method gave the lowest classification error. In order to evaluate the performance of different SRC for M-FISH imaging analysis, three different sparse representation methods, namely, Homotopy method, Orthogonal Matching Pursuit (OMP), and Least Angle Regression (LARS), were tested and compared. Results from our statistical analysis have shown that Homotopy based method is significantly better than the other two methods. Our work indicates that sparse representations based classifiers with proper models can outperform many existing classifiers for M-FISH classification including those that we proposed before, which can significantly improve the multicolor imaging system for chromosome analysis in cancer and genetic disease diagnosis.