ABSTRACT
We assume the data are composed of a small number L of projections of a 3D unknown curve, say C*, (L < 10 in our application). The projection images are very degraded: each observed projection of the curve C* is not a binary image of a 2D curve, but is a grey level image digitized on a square grid S£. Such an image can be seen as a blurred projection, or in other words as a plane having discontinuities represented by an uneven valley in which the theoretical curve projection of C* lies approximately in the bottom, [1]. Furthermore, due to the degradation, the valley may be the union of several valleys. For the images g = {<7^ i = 1, L } we assume that E (g£) < 0 if the site s £ S£ belongs to a valley, and E (g£) = 0 otherwise, E stands for the mathematical expectation. Note that we do not assume any knowledge about the physical degradation system. We denote by { V £, i = 1,..., L} the geometrical projection functions on the image planes. For instance, in our application each V 1 is defined from a point source 0 £ which illuminates the curves C* with a 3D fan-beam of 7rays. Denoting S£ the projection plane associated to the source O e, for every point cGC*, the non-degraded projection is simply V £(c) = S£ Π O^c, where 0 £c is the ray emitted by 0 £ and passing through c.
