A thorough investigation of the application of support vector regression (SVR) to the superresolution problem is conducted through various frameworks. Prior to the study, the SVR problem is enhanced by finding the optimal kernel. This is done by formulating the kernel learning problem in SVR form as a convex optimization problem, specifically a semi-definite programming (SDP) problem. An additional constraint is added to reduce the SDP to a quadratically constrained quadratic programming (QCQP) problem. After this optimization, investigation of the relevancy of SVR to superresolution proceeds with the possibility of using a single and general support vector regression for all image content, and the results are impressive for small training sets. This idea is improved upon by observing structural properties in the discrete cosine transform (DCT) domain to aid in learning the regression. Further improvement involves a combination of classification and SVR-based techniques, extending works in resolution synthesis. This method, termed kernel resolution synthesis, uses specific regressors for isolated image content to describe the domain through a partitioned look of the vector space, thereby yielding good results.