A MAP estimation algorithm using IIR recursive filters

Abstract

The MAP method is a wide spread estimation technique used in many signal processing problems, e.g., image restoration, denoising and 3D reconstruction. When there is a large number of variables to estimate, the MAP method often leads to a huge set of linear or non-linear equations which must be numerically solved using time consuming algorithms. This paper proposes a fast method to compute the MAP estimates in large scale problems, based on the solution of a linear set of equations by low pass filtering the ML solution. A family of space varying UR filters with data dependent coefficients is derived from the MAP criterion. This approach can be extended to other types of filters derived under different assumptions about the prior or using other design strategies. The filter approach proposed in this paper is much faster than the classic solution and provides additional insights about the structure of the problem. Experimental results are provided to assess the performance of the proposed methods with Gaussian and non Gaussian noise models. © Springer-Verlag Berlin Heidelberg 2003.