The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated that structured signals can be acquired with just a small number of linear measurements, on the order

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Abstract — We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing kernel Hilbert spaces (RKHS). After a characterization of the RKHS associated with the SLGM, we derive a lower bound on the minimum variance achievable by estimators with a prescribed bias function, including the important special case of unbiased estimation. This bound is obtained via an orthogonal projection of the prescribed mean function onto a subspace of the RKHS associated with the SLGM. It provides an approximation to the minimum achievable variance (Barankin bound) that is tighter than any known bound. Our bound holds for an arbitrary system matrix, including the overdetermined and underdetermined cases. We specialize

m]]l]]s¶D]]¿÷mB]iv]b]oD]m¶¨]iv]§]iv]r]j]t¿rv]]irj]]t]]m] / | ap]]r¿]ÎNy]s¶D]]mb¶r]ix} Û]Ix]]rd]mb]} p—N]t]o%ism] in]ty]m] / || Û]Is]¡uÎc]rN]]riv]nd]p]*N]m]st¶ I always bow to Śri ̄ Śāradāmbā, the limitless ocean of the nectar of compassion, who bears a rosary, a vessel of nectar, the symbol of knowledge and a book in Her lotus hands. Dedicated to the Lotus Feet of the revered Sadguru. This thesis presents a new active mask (AM) framework and an algorithm for segmenta-tion of digital images, particularly those of punctate patterns from fluorescence microscopy. Fluorescence microscopy has greatly facilitated the task of understanding complex sys-tems at cellular and molecular levels in recent years. Segmentation, an important yet dif-ficult problem, is often the first processing step following acquisition. Our team previously demonstrated that a stochastic active contour based algorithm together with the concept of

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