This paper proposes the application of learned kernels in support vector regression to superresolution in the discrete cosine transform (DCT) domain. Though previous works involve kernel learning, their problem formulation is examined to reformulate the semi-definite programming problem of finding the optimal kernel matrix. For the particular application to superresolution, downsampling properties derived in the DCT domain are exploited to add structure to the learning algorithm. The advantage of the proposed method over other learning-based superresolution algorithms include specificity with regard to image content, structured consideration of energy compaction, and the added degrees of freedom that regression has over classification-based algorithms