The non-convex sparse problem with nonnegative constraint for signal reconstruction
The subject of the article is located in a scientifically active area of finding a sparse solution for linear equations. It usually includes a formulation into a combinatorial optimization problem which is usually relaxed as a convex or a non-convex problem. The authors investigate the non-convex problem with the nonnegative constraint which has an application in signal reconstruction. They consider obtaining Lipschitz continuous problem from the non-Lipschitz one to reduce the computational complexity of the original problem and develop a fast algorithm based on the limited-memory BFGS algorithm to find its sparse solution. They show that the proposed algorithm has better or comparable performance in terms of the CPU time by producing more sparse solutions than convex methods or non-convex methods. This article is well written, structured and explained, it contains five sections: Section 1 Introduction, Section 2 Preliminaries, Section 3 A reformulation, Section 4 Algorithm description, and Section 5 Numerical illustrations, and Section 6 Conclusion. In fact, future scientific work on other application fields such as face recognition and image signal decomposition as well as investigating the equivalence relationship would be interesting.
scientific article; zbMATH DE number 6641402
scientific article