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Full-Text Articles in Physical Sciences and Mathematics
A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu
A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu
CMC Faculty Publications and Research
Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many socalled signal space methods have been developed to extend this body of work to signals sparse in arbitrary dictionaries rather than orthonormal bases. In doing so, CS can be utilized in a much broader array of practical settings. Often, such approaches often rely on the ability to optimally project a signal onto a small number of dictionary atoms. Such optimal, or even approximate, projections have been difficult to derive theoretically. Nonetheless, it has …
Compressive Sensing With Redundant Dictionaries And Structured Measurements, Felix Krahmer, Deanna Needell, Rachel Ward
Compressive Sensing With Redundant Dictionaries And Structured Measurements, Felix Krahmer, Deanna Needell, Rachel Ward
CMC Faculty Publications and Research
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary D. This problem is now understood to be well-posed and efficiently solvable under suitable assumptions on the measurements and dictionary, if the number of measurements scales roughly with the sparsity level. One sufficient condition for such is the D-restricted isometry property (D-RIP), which asks that the sampling matrix approximately preserve the norm of all signals which are sufficiently sparse in D. While many classes of random matrices are known to satisfy such conditions, such matrices …
One-Bit Compressive Sensing With Partial Support, Phillip North, Deanna Needell
One-Bit Compressive Sensing With Partial Support, Phillip North, Deanna Needell
CMC Faculty Publications and Research
The Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization, as is exemplified by the so-called one-bit compressed sensing framework which aims to recover a signal from measurements reduced to only their sign-bit. In applications, it is often the case that we have some knowledge of the structure of the signal beforehand, and thus would like to leverage it to attain more accurate and efficient recovery. This work explores avenues for incorporating such partial support information into the one-bit setting. Experimental results demonstrate that newly proposed methods of this work yield improved signal recovery …