On the reconstruction of an image from its moments

An image can be seen as an element of a vector space so that it can be expressed in terms of a series expansion of any non necessarily orthogonal base of this space. This paper shows how a matrix-based formulation of this fact permits deriving a new reconstruction method of an image from its geometric moments where the basis functions used in the reconstruction and those used to obtain the moments do not necessarily define the same subspace. This permits introducing constraints relative to the bandwidth or the spatial resolution of the image to be reconstructed. Moreover, it is shown that, by exploiting the algebraic properties of the involved matrices as well as the properties of computer arithmetic, accurate solutions to this problem in spite of its ill-conditioning can be obtained.