Variational principles applied to image filtering

In this paper we present a novel image filtering and reconstruction methodology mathematically supported by variational principles and partial diferential equations. We will establish the uni-dimensional formulation of the technique which gives sufficient insight about its use and is far easier to state and implement than the bi-dimensional one and has obvious computational advantages over the latter approach. Some considerations about the bi-dimensional formulation and its relation to the uni-dimensional one will be given.