Robust Multiresolution Techniques for Image Reconstruction

The reconstruction of images from projections, diffraction fields, or other similar measurements requires applying signal processing techniques within a physical context. Although modeling of the acquisition procedure can conveniently be carried out in the continuous domain, actual reconstruction from experimental measurements requires the derivation of discrete algorithms that are accurate, efficient, and robust. In recent years, wavelets and multiresolution approaches have been applied successfully for common image processing tasks bridging the gap between discrete and continuous repre-sentations. We show that it is possible to express many physical problems in a wavelet framework, thereby allowing the derivation of efficient algorithms that take advantage of wavelet properties, such as multiresolution structure, sparsity, and space-frequency decompositions. We review several examples of such algorithms with applications to X-ray tomography, digital holography, and confocal microscopy and discuss possible future extensions to other modalities