Least squares and total least squares methods in image restoration

Abstract

Image restoration is the process of removing or minimizing degradations (blur) in an image. Mathematically, it can be modeled as a discrete ill-posed problem Hf=g, where H is a matrix of large dimension representing the blurring phenomena, and g is a vector representing the observed image. Often H is severely ill-conditioned, and both H and g are corrupted with noise. Regularization is used to reduce the noise sensitivity of the numerical scheme. Most of these methods, however, assume that there is no noise in H, and therefore least squares techniques are used to reconstruct f. In some applications, though, H is also corrupted with noise. In this case a total least squares approach may be more appropriate. These least squares and total least squares methods will be investigated in the context of signal restoration.