Real-time reconstruction of 2D signals with missing observations

This paper describes real time methods to restore two dimensional (2D) uniformly sampled signals with randomly missing observations. It is based upon auto regressive (AR) modeling. The model parameters are estimated by means of an LMS-like algorithm adapted to the case of the non uniform context. Missing samples are replaced by their estimate. The criterion used to perform an optimal estimation is defined only when samples are available. Missing observations lead to a non quadratic criterion, unlike the uniform sampling. Two approximations of the criterion are proposed. They lead to two types of algorithms. Considering different 2D signal causalities, delayed and non delayed versions of those algorithms can be obtained. In this paper, some formal descriptions of the algorithms are presented. Their reconstruction performance (in terms of signal-to-error ratio) are compared as functions of the percentage of lost samples.