Uniform recovery from subgaussian multi-sensor measurements |
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Institution: | 1. Department of Electrical Engineering and Computer Science, University of Michigan, USA;2. Department of Mathematics, Simon Fraser University, Canada;1. Leiden University, Netherlands;2. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France;1. Department of Mathematics, Vanderbilt University, Nashville, TN, 37212, USA;2. Department of Mathematical Science, Northern Illinois University, Dekalb, IL, 60115, USA;3. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA |
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Abstract: | Parallel acquisition systems are employed successfully in a variety of different sensing applications when a single sensor cannot provide enough measurements for a high-quality reconstruction. In this paper, we consider compressed sensing (CS) for parallel acquisition systems when the individual sensors use subgaussian random sampling. Our main results are a series of uniform recovery guarantees which relate the number of measurements required to the basis in which the solution is sparse and certain characteristics of the multi-sensor system, known as sensor profile matrices. In particular, we derive sufficient conditions for optimal recovery, in the sense that the number of measurements required per sensor decreases linearly with the total number of sensors, and demonstrate explicit examples of multi-sensor systems for which this holds. We establish these results by proving the so-called Asymmetric Restricted Isometry Property (ARIP) for the sensing system and use this to derive both nonuniversal and universal recovery guarantees. Compared to existing work, our results not only lead to better stability and robustness estimates but also provide simpler and sharper constants in the measurement conditions. Finally, we show how the problem of CS with block-diagonal sensing matrices can be viewed as a particular case of our multi-sensor framework. Specializing our results to this setting leads to a recovery guarantee that is at least as good as existing results. |
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Keywords: | Compressed sensing Multi-sensor system Parallel acquisition Subgaussian random sampling Uniform recovery Asymmetric restricted isometry property Block-diagonal sensing |
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