Stabilized algorithms for ill-posed problems in signal processing

In this paper we discuss two kinds of ill-posed problems in signal processing, that is, in detail, reconstructing compactly supported signals in the Fourier transform and solving the convolution equation with analytic kernel. Having analyzed the essential reason of ill-posedness for these problems, we present some stabilized algorithms, which cure the ill-posedness, to recover the approximate solution. Finally numerical experiments show the efficiency and fast convergence of these algorithms.