Grey-level intensity measurements processing by means of Volterra equations and Least Squares Method for Video restoration

Abstract

In this paper a video sequence is considered as a two dimensional time evolving process. Under this assumption two Volterra equations based mathematical models are introduced for video restoration purposes. The first one is based on geometric features related to the spatial--time structure of the video sequence and gives rise to a nonlinear Volterra equation. This model arises from the Mean Curvature Flow linked to evolving surfaces. The second one is based on analytic features and leads to the formulation of a linear Volterra model. The second procedure relies on the assumption of local time coherence in the sequence of frames, at least short back in time. In both cases \red{Volterra equations based approach introduces a memory effect in the process which in the present terminology means that several frames back may be taken into account for the better reconstruction of the current frame throughout a convenient choice of the convolution kernel. On the other hand the role played by Least Squares Method focuses on the practical computation of that convolution kernel just at discrete level.} The performance of both approaches is shown through a list of suitable experiments, and the better performance of the second approach is illustrated with remarkable improvements in critical cases.