Application of the Regularization Method

In this book the concepts of ill-posed problems and regularization methods are introduced. The ill-posedness of the sampling problem computation of the Fourier transform restoring lost samples and the low pass filter is discussed. The regularization method is imported to solve these ill-posed problems. The regularized solutions are given by weight functions instead of the Tikhonov regularization by finding the minimum of a smoothing functional. Both the proof and numerical results are given.