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Self-reset analog-to-digital converters (ADCs) allow for digitization of a signal with a high dynamic range. The reset action is equivalent to a modulo operation performed on the signal. We consider the problem of recovering the original signal from the measured modulo-operated signal. In our formulation, we assume that the underlying signal is Lipschitz continuous. The modulo-operated signal can be expressed as the sum of the original signal and a piecewise-constant signal that captures the transitions. The reconstruction requires estimating the piecewise-constant signal.

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It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard. We formularize the problem as the experimental design of a linear regression model if we allow multiple measurements on a single node. By relaxing it to a convex optimization problem, we get the proportion of sample for each node given the budget of total sample size. Then, we use a probabilistic quantization to get the number of each node to be sampled.

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In an optical imaging system, the retrieved image of an object is blurred by the point spread function (PSF) of the system,and cannot exactly represent the object. Deconvolution is an effective method to recover the object from the blurred image and improve the resolution of the optical system. But in real optical system, the detector only measures the intensity of the light, not the phase.

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Compressive information acquisition is a natural approach for low-power hardware front ends, since most natural signals are sparse in some basis. Key design questions include the impact of hardware impairments (e.g., nonlinearities) and constraints (e.g., spatially localized computations) on the fidelity of information acquisition. Our goal in this paper is to obtain specific insights into such issues through modeling of a Large Area Electronics (LAE)-based image acquisition system.

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We consider demixing a pair of sparse signals in orthonormal basis via convex optimization. Theoretically, we characterize the condition under which the solution of the convex optimization problem correctly demixes the true signal components. In specific, we introduce the local subspace coherence to characterize how a basis vector is coherent with a signal subspace, and show that the convex optimization approach succeeds if the subspaces of the true signal components avoid high local subspace coherence.

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