Singular value decomposition, singular vectors, and the discrete prolate spheroidal sequences

We study in this paper a discrete-time, discrete-frequency model for image restoration using the singular value decomposition of the imaging matrix. We show that the resulting singular vectors have many of the properties possessed by Slepian´s discrete prolate sphroidal sequences (DPSS). They are doubly orthogonal, they are bandlimited, they satisfy an equation very similar to that satisfied by the DPSSs, and they possess an extremal energy-concentration property. These properties continue to hold with appropriate modification for bandpass as well as lowpass operations.