Image Reconstruction and Partial Deconvolution with Support Constraint Separation Angle and Least-Squares Interpolation Procedures

Abstract

In image reconstruction from projections [1], and more generally, in any partial deconvolution with support constraint, the central problem is to specify the conditions under which it is possible to interpolate, in a bounded region W, the Fourier transform of an object function with support in a bounded region V [2,3,4]. In particular, it is then essential to understand, in an analytical way, the parts played by the size of V and W, and the geometry of the whole V, W-configuration (cf. for example Fig. 1). The aim of this communication is to summarize the corresponding analysis, and to visualize the main results with the aid of appropriate representations.