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Publication# A Learning-Based Framework for Quantized Compressed Sensing

Résumé

Sparse recovery from undersampled random quan- tization measurements is a recent active research topic. Previous work asserts that stable recovery can be guaranteed via the basis pursuit dequantizer (BPDQ) if the measurements number is large enough, considering random sampling patterns. In this paper, we study a learning-based method for optimizing the sampling pattern, within the framework of sparse recovery via BPDQ from their uniformly quantized measurements. Given a set of representative training signals, the method finds the sampling pattern that performs the best on average over these signals. We compare our approach with the random sampling and other state-of-the-art sampling methods, which shows that it achieves superior reconstruction performance. We demonstrate that proper accounting for sampling and careful sampler de- sign has a significant impact on the performance of quantized compressive sensing methods.

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Concepts associés (31)

MOOCs associés (8)

Publications associées (52)

Simple random sample

In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. A simple random sample is an unbiased sampling technique. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods.

Nonprobability sampling

Sampling is the use of a subset of the population to represent the whole population or to inform about (social) processes that are meaningful beyond the particular cases, individuals or sites studied. Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular sample may be calculated. In cases where external validity is not of critical importance to the study's goals or purpose, researchers might prefer to use nonprobability sampling.

Systematic sampling

In survey methodology, systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equiprobability method. In this approach, progression through the list is treated circularly, with a return to the top once the list ends. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, is the sampling interval (sometimes known as the skip): this is calculated as: where n is the sample size, and N is the population size.

Digital Signal Processing I

Basic signal processing concepts, Fourier analysis and filters. This module can
be used as a starting point or a basic refresher in elementary DSP

Digital Signal Processing II

Adaptive signal processing, A/D and D/A. This module provides the basic
tools for adaptive filtering and a solid mathematical framework for sampling and
quantization

Digital Signal Processing III

Advanced topics: this module covers real-time audio processing (with
examples on a hardware board), image processing and communication system design.

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