We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class () of multiband signals with spectral support , at rates arbitrarily close to the Landau minimum rate equal to the Lebesgue measure of , even when does not tile under translation. Using the conditions for exact reconstruction, we derive an explicit reconstruction formula. We compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band-limited to the "span of " (the smallest interval containing) which is a bigger class than the valid signals (), band-limited to. We also examine the performance of the reconstruction system when the input contains additive sample noise.

An achievable region for the -channel multiple description coding problem is presented. This region generalizes twochannel results of El Gamal and Cover and of Zhang and Berger. It further generalizes three-channel results of Gray and Wyner and of Zhang and Berger. A source that is successively refinable on chains is shown to be successively refinable on trees. A new outer bound on the rate-distortion (RD) region for memoryless Gaussian sources with mean squared error distortion is also derived. The achievable region meets this outer bound for certain symmetric cases.

We study the problem of optimal sub-Nyquist sampling for perfect reconstruction of multiband signals. The signals are assumed to have a known spectral support that does not tile under translation. Such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching Landau's lower bound equal to the measure of. For signals with sparse , this rate can be much smaller than the Nyquist rate. Unfortunately, the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In a recent study, we derived bounds on the error due to mismodeling and sample additive noise. Adopting these bounds as performance measures, we consider the problems of optimizing the reconstruction sections of the system, choosing the optimal base sampling rate, and designing the nonuniform sampling pattern. We find that optimizing these parameters can improve system performance significantly. Furthermore, uniform sampling is optimal for signals with that tiles under translation. For signals with nontiling , which are not amenable to efficient uniform sampling, the results reveal increased error sensitivities with sub-Nyquist sampling. However, these can be controlled by optimal design, demonstrating the potential for practical multifold reductions in sampling rate.

We address the problem of sampling of 2D signals with sparse multi-band spectral structure. We show that the signal can be sampled at a fraction of the its Nyquist density determined by the occupancy of the signal in its frequency domain, but without explicit knowledge of its spectral structure. We nd that such a signal can almost surely be reconstructed from its multi-coset samples provided that a universal pattern is used. Also, the scheme can attain the Landau-Nyquist minimum density asymptotically. The spectrum blind feature of our reconstruction scheme has potential applications in Fourier imaging. We apply the sampling scheme on a test image to demonstrate its performance.

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