Regularization is the approximation of an ill-posed problem by a family of neighbouring well-posed problems. There are various regularization methods found in the literature depending on the choice of L(x). The aim is to find the best-approximate solution x δ of Kx = y in the situation that the 'noiseless data' y are not known precisely but that only a noisy representation y δ with ||y δ - y|| ≤ δ is available. Typically y δ would be the real (noisy) signal. In general, an xαδ is found which minimizes
