Solution of the Discrete Ill-Posed Problem on the Basis of Singular Value Decomposition and Random Projection

Abstract

A brief overview of our work on the solution of DIP is presented. The stable solution of DIP we obtained, by truncated singular value decomposition and by random projection methods. Analytic and experimental averaging over random matrices for the evaluation of the error of true signal recovery is carried out for the method of solving the discrete ill-posed problems on the basis of random projection. Averaging over random matrices leads to diagonalization of the matrix conditioning both components of the error (deterministic and stochastic). The values of the diagonal elements change monotonically as a function of k. This in turn leads to the smoother characteristics and reducing the number of local minima. The results of the experimental study showed the connection of the elements of the diagonalized matrix with the singular values of the original matrix. This provides the basis for investigating the connection of the truncated singular value decomposition method and the random projection method.