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We address the problem of computing joint sparse representation of visual signal across multiple kernel-based representations. Such a problem arises naturally in supervised visual recognition applications where one aims to reconstruct a test sample with multiple features from as few training subjects as possible. We cast the linear version of this problem into a multi-task joint covariate selection model, which can be very efficiently optimized via ker-nelizable accelerated proximal gradient method. Furthermore, two kernel-view extensions of this method are provided to handle the situations where descriptors and similarity functions are in the form of kernel matrices. We then investigate into two applications of our algorithm to feature combination: 1) fusing gray-level and LBP features for face recognition, and 2) combining multiple kernels for object categorization. Experimental results on challenging real-world datasets show that the feature combination capability of our proposed algorithm is competitive to the state-of-the-art multiple kernel learning methods.