Each year more and more people are diagnosed with Diabetes Mellitus. As this disease continues to grow, it will have an enormous effect on society. Recently, a computerized noninvasive diagnostic method was proposed using facial block color features with a sparse representation classifier. This method eliminated the need to extract bodily fluids, and any feelings of pain and discomfort associated with a Fasting Plasma Glucose test. Though its result is promising and the detection can be considered to be accurate, there is still much room for improvement and increment in the diagnostic accuracy. In addition, the effects of sparse representation have not been extensively investigated for this application. In this paper a study of sparse representation algorithms is carried out to determine its effectiveness at distinguishing facial block(s) from two classes, Diabetes Mellitus and Healthy. Four groups of sparse representation algorithms are examined. They include greedy strategy approximation, constrained optimization strategy, proximity algorithm based optimization strategy, and homotopy algorithm based sparse representation. Facial block color features are extracted and used with a representative method from each group to perform classification. The experimental results show that the orthogonal matching pursuit algorithm from the greedy strategy approximation group achieves the best performance of 99.65%-sensitivity, 97.93%-specificity, and 99.06%- A ccuracy at discriminating individuals from either class using their facial block(s).