Abstract:

A reconstruction problem of function from integral average values with perturbation is considered, and propose a type of reconstruction method. From the abstract operator equation, we analyze and solve this type of problem, and show that the solution operator is bounded regardless of the grid size. Therefore the problem under consideration is well-posed. The method of solving this problem does not need regularization, thus greatly simplifying the algorithm. Numerical results show that the method is effective. 

Key words: integral average value; reconstruction of function; boundedness of solution operator; well-posed; error analysis