The Sparse Solution Of Nonlinear Least Square

The sparse solution of the least square problem has played an important role in the signal and image processing, which gets lots of attention. The sparse solution of the least square problem gets lots of attention. In the area of signal transmission, image compression, pattern recognition. There are a lot of effective methods to solve the sparse solution of the linear least square problem. In this paper, we approximate the zero norm using the p norm, construct the smooth function about the p norm according to the nonlinear least square sparse solutions.In the first chapter, we introduce the bases of the paper, including the based model about mathematical programming and the least square problem, the common methods to solve the sparse solution of the linear least square problem, the development process of the homotopy method, the common smooth functions, and smooth the p norm to get a smooth model for approximating the sparse solution of the nonlinear least square problem.In the second chapter, we first establish the Lagrange function and the Karush-Kuhn-Tucker system, then give the combined homotopy mapping about the smooth model. We prove that the smooth functions satisfy the condition of making the homotopy path exist and converge, present the existence and global convergence of a homotopy path.In the third chapter, we present the combined homotopy algorithm corresponding to the sparse solution of the nonlinear least square problem.In the fourth chapter, we design the tracking path algorithm by using the predictor-corrector method. Numerical results indicate that the two smooth functions are feasible. Besides, numerical performances on corresponding to the two smooth functions are compared through experiments.