A Wavelet Approach Fitting to Signals in Multi-exponential Decay

This paper is about to solve a multiexponential decay fitting, which is equivalent to an improper problem, called Fredholm integral equation of the first kind. The thought of Multi-resolution analysis of wavelet analysis has been applied here. In order to solve the specific problems, this paper managed to extract the feature of matrix essentially by ignoring the detail information of the large matrix. We solve the problem after dividing the matrix and vectors into blocks, and obtain a set of fuzzy solution for the original problem. Then we remove several weaker components and solve the problem using singular value decomposition. This method eventually greatly reduces the complexity and improves the solution accuracy and speeds up the solution.