A New Method Of Computed Generalized Inverse In Application Of Image Restoration

The theory and methods of generalized inverse matrices are important basis tools in all mathematical disciplines and have extensive applications in economics statistics, surveying, optimization techniques, information processing, automatic control, engineering techniques, operations research and so on. On the other hand, the study of algebra structure of associative ring is prevalent, and matrices generalized inverse over a ring is an important tool in revealing algebra structure of associative ring.In this paper, first introduced rang, null space and generalized inverse of the rank theoretical knowledge, designated rang and null space the generalized inverse, said the specific expositions. Through expression theory of generalized inverse and matrix factorization, mainly, study generalized inverse calculation. We will study and settle following several problems.The first, it is celebrated that Gauss-Jordan elimination method compute the inverse of a nonsingular matrix by executing elementary row (or column) operation. Moreover the operation can be used to determine whether or not a matrix is nonsingular. However, one cannot directly use this method on a generalized inverse of a rectangular matrix or a square singular matrix. In this paper, said here on expression of the generalized inverse of a number of improvements, Gauss-Jordan elimination method so that it can be used to solve.The second, image restoration is an ill posed problem and must be regularized. Usually, the difficulty of regularization lies in avoiding the smoothing of edges while suppressing the noise. The improver algorithm of edge- preserving regularization used the new solution of the generalized inverse, thus comparing to the original method, it shows its effectiveness.