Diabetic retinopathy (DR) is the main cause of blindness in diabetic patients. Early and accurate diagnosis can improve the analysis and prognosis of the disease. One of the earliest symptoms of DR are the hemorrhages in the retina. Therefore, we propose a new method for accurate hemorrhage detection from the retinal fundus images. First, the proposed method uses the modified contrast enhancement method to improve the edge details from the input retinal fundus images. In the second stage, a new convolutional neural network (CNN) architecture is proposed to detect hemorrhages. A modified pre-trained CNN model is used to extract features from the detected hemorrhages. In the third stage, all extracted feature vectors are fused using the convolutional sparse image decomposition method, and finally, the best features are selected by using the multi-logistic regression controlled entropy variance approach. The proposed method is evaluated on 1509 images from HRF, DRIVE, STARE, MESSIDOR, DIARETDB0, and DIARETDB1 databases and achieves the average accuracy of 97.71%, which is superior to the previous works. Moreover, the proposed hemorrhage detection system attains better performance, in terms of visual quality and quantitative analysis with high accuracy, in comparison with the state-of-the-art methods.