Image restoration by convex projections: Application to image spectrometry

We present a new algorithm for image restoration with application to image spectrometry, combining two radically different techniques: the singular value decomposition (SVD) and the method of projections onto convex sets (POCS). The SVD technique is used to obtain an initial estimate of the unknown image and to establish correspondence between the missing data and the spectral description of the image. The iterative method of cons ex projections is then applied to the estimate, regaining the missing data by enforcing a sequence of constraints on the reconstructed object. We report results of investigations of the SVD-POCS method and demonstrate that the new algorithm leads to significant improvements in the recovered image.