Difference of Convex Functions Algorithm (DCA) for Compressed Sensing Biomedical Imaging Applications

The difference of convex functions algorithm (DCA) using the concave-convex procedure (CCCP) is a class of optimization algorithms that address minimization problems represented as the difference of two convex functions. In DCA, even though the original problem is not jointly convex, each subproblem can be represented as a convex problem. Moreover, the convergence behavior of DCA has been well-studied. In this talk, I will show that many interesting biomedical imaging problems with concave or convex prior can be formulated as the difference of convex functions, which can be addressed using DCA. Then, I will describe our recent applications of DCA to dynamic MRI using patch regularization and super-resolution microscopy using Poisson noise model. Finally, I will briefly discuss about the relationship between DCA and the majorization-minimization method.