Computer-assisted automated exudate detection is crucial for large-scale screening of diabetic retinopathy (DR). The motivation of this work is robust and accurate detection of low contrast and isolated hard exudates using fundus imaging. Gabor filtering is first performed to enhance exudate visibility followed by Tsallis entropy thresholding. The obtained candidate exudate pixel map is useful for further removal of falsely detected candidates using sparse-based dictionary learning and classification. Two reconstructive dictionaries are learnt using the intensity, gradient, local energy, and transform domain features extracted from exudate and background patches of the training fundus images. Then, a sparse representation-based classifier separates the true exudate pixels from false positives using least reconstruction error. The proposed method is evaluated on the publicly available e-ophtha EX and standard DR database calibration level 1 (DIARETDB1) databases and high exudate detection performance is achieved. In the e-ophtha EX database, mean sensitivity of 85.80% and positive predictive value of 57.93% are found. For the DIARETDB1 database, an area under the curve of 0.954 is obtained.