alexa Encoding the  p Ball from Limited Measurements
Engineering

Engineering

Biosensors Journal

Author(s): Emmanuel Cand e, Justin Romberg

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We address the problem of encoding signals which are sparse , i.e. signals that are concentrated on a set of small support. Mathematically, such signals are modeled as elements in the  p ball for some p ≤ 1. We describe a strategy for encoding elements of the  p ball which is universal in that 1) the encoding procedure is completely generic, and does not depend on p (the sparsity of the signal), and 2) it achieves near-optimal minimax performance simultaneously for all p< 1. What makes our coding procedure unique is that it requires only a limited number of nonadaptive measurements of the underlying sparse signal; we show that near-optimal performance can be obtained with a number of measurements that is roughly proportional to the number of bits used by the encoder. We end by briefly discussing these results in the context of image compression.

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This article was published in Proceedings of the Data Compression Conference and referenced in Biosensors Journal

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