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—Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non-adaptive linear projection observations, provided that the objects possess a sparse representation in some basis. Subsequent efforts have shown that the performance of CS can be… (More)

Poisson processes are commonly used models for describing discrete arrival phenomena arising, for example, in photon-limited scenarios in low-light and infrared imaging, astronomy, and nuclear medicine applications. In this context, several recent efforts have evaluated Poisson denoising methods that utilize contemporary sparse modeling and dictionary… (More)

This paper examines a general class of noisy matrix completion tasks, where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is on settings where the matrix to be estimated is well-approximated by a product of two (a priori unknown) matrices,… (More)

Recent breakthrough results in compressive sensing (CS) have established that many high dimensional signals can be accurately recovered from a relatively small number of non-adaptive linear observations, provided that the signals possess a sparse representation in some basis. Subsequent efforts have shown that the performance of CS can be improved by… (More)

Breakthrough results in compressive sensing (CS) have shown that high dimensional signals (vectors) can often be accurately recovered from a relatively small number of non-adaptive linear projection observations, provided that they possess a sparse representation in some basis. Subsequent efforts have established that the reconstruction performance of CS… (More)

—This work investigates the task of estimating an unknown signal (vector) from compressive measurements corrupted by additive pre-measurement noise (" clutter ") as well as post-measurement noise, in the case where some perhaps limited prior knowledge on the signal, clutter , and noise is available. We pose the overall problem as an optimization whose goal… (More)

This paper examines a general class of matrix completion tasks where entry wise observations of the matrix are subject to random noise or corruption. Our particular focus here is on settings where the matrix to be estimated follows a sparse factor model, in the sense that it may be expressed as the product of two matrices, one of which is sparse. We analyze… (More)

Biological sequence comparison is a key step in inferring the relatedness of various organisms and the functional similarity of their components. Thanks to the Next Generation Sequencing efforts, an abundance of sequence data is now available to be processed for a range of bioinformatics applications. Embedding a biological sequence – over a nucleotide or… (More)

—This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or " clutter ") as well as post-measurement noise, in the specific setting where some (perhaps limited) prior knowledge on the signal, interference,… (More)