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The application that motivates this paper is molecular imaging at the atomic level. When discretized at subatomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution of the image with the system point spread function (psf). Such is the case with magnetic resonance force microscopy… (More)

Sparse image reconstruction is of interest in the fields of radioas-tronomy and molecular imaging. The observation is assumed to be a linear transformation of the image, and corrupted by additive white Gaussian noise. We study the usage of sparse priors in the empirical Bayes framework: it permits the selection of the hyperparameters of the prior in a… (More)

—Detection of a finite-state Markov signal in additive white Gaussian noise (AWGN) can be done in an intuitive manner by applying an appropriate filter and using an energy detector. One might not expect this heuristic approach to signal detection to be optimal. However, in this paper, we show that for a certain type of finite-state Markov signal, namely,… (More)

This paper considers the detection of a Markov signal in additive white Gaussian noise (AWGN). Here, the Markov signal is taken to be a certain class of random walk processes. A closed form expression of the likelihood ratio (LR) is derived for a general Markov signal in AWGN. Then, under the conditions of low signal to noise ratio (SNR) and long… (More)

The focus of this paper is the optimal detection of piecewise constant binary valued continuous-time (C-T) signals with Markovian state transitions. One example is the classic random telegraph signal for which the number of states is two and the transitions follow a Poisson process. This signal detection problem arises in many different areas of engineering… (More)

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