关键词: 稀疏逼近;压缩感知;最优化;重构

Abstract:

In image processing and statistics,to find a sparse approximate solution for a large underdetermined linear equation is a common problem.The standard method is to look for the minimum value of an objective function,which includes a quadratic l₂ error term added to a regularizer l₂.For the more general problem,we propose an algorithm,where the objective function is made up of a smooth convex function and a nonsmooth regularizer.The algorithm obtains the sparse approximate solution by solving the optimal sub-problems.The simulation result shows that the algorithm can find the approximate solution quickly and the minima solution of the function is convergent under the conditions namely convexity of the regularizer.

Key words: sparse approximation;compressed sensing;optimization;reconstruction