This work presents a novel compressed learning framework designed for optimized image sampling for clas-sification tasks. In this study, we replace the conventional random sampling method in classical compressed sensing with an optimization-based approach to derive a specific sensing mask that maximizes classification accuracy within a dataset. The proposed approach recognizes and uses structural information from input images for sampling, specifically relevant to the downstream task. Leveraging a genetic algorithm as an optimizer within the framework, we aim to improve the classification performance of a pre-trained convolutional neural network by enhancing the sensing mask. Two benchmark datasets, MNIST and Fashion MNIST, are used for performance evaluation. In addition to the masking, the framework is tested in a traditional sensing setup with sensing matrix optimization. The results suggest that optimization-based sampling could be a good alternative to random sampling in compressed sensing due to its superior performance.