14.4.5 Object representation space

The reconstructed image is defined as the function $\Phi _E$of the object space H_o minimizing some objective functional. The definition of this functional takes into account the nature of the data, as well as other constraints. For example, the image to be reconstructed may be confined to a subspace, or more generally to a convex set, of the object space H_o: this convex set is the object representation space E. It may be defined from the outset (in an interactive manner, for example), or step by step throughout the image reconstruction procedure (this is the case of the current implementation of WIPE). In both cases, the projection operator onto this space, the projector P_E, will play an essential role in the image reconstruction process.

REMARK 1: positivity constraint.

In most cases encountered in practice, the scalar components of $\Phi _E$in the interpolation basis of H_o must be non-negative (cf. Eq.14.2). In the current implementation of WIPE this constraint is taken into account. The object representation space E is then built, step by step, accordingly.