English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper studies the problem of reconstructing sparse or compressiblesignals from compressed sensing measurements that have undergone nonuniformquantization. Previous approaches to this Quantized Compressed Sensing (QCS)problem based on Gaussian models (bounded l2-norm) for the quantizationdistortion yield results that, while often acceptable, may not be fullyconsistent: re-measurement and quantization of the reconstructed signal do notnecessarily match the initial observations. Quantization distortion insteadmore closely resembles heteroscedastic uniform noise, with variance dependingon the observed quantization bin. Generalizing our previous work on uniformquantization, we show that for nonuniform quantizers described by the"compander" formalism, quantization distortion may be better characterized ashaving bounded weighted lp-norm (p >= 2), for a particular weighting. Wedevelop a new reconstruction approach, termed Generalized Basis Pursuit DeNoise(GBPDN), which minimizes the sparsity of the reconstructed signal under thisweighted lp-norm fidelity constraint. We prove that for B bits per measurementand under the oversampled QCS scenario (when the number of measurements islarge compared to the signal sparsity) if the sensing matrix satisfies aproposed generalized Restricted Isometry Property, then, GBPDN provides areconstruction error of sparse signals which decreases likeO(2^{-B}/\sqrt{p+1}): a reduction by a factor \sqrt{p+1} relative to thatproduced by using the l2-norm. Besides the QCS scenario, we also show thatGBPDN applies straightforwardly to the related case of CS measurementscorrupted by heteroscedastic Generalized Gaussian noise with provablereconstruction error reduction. Finally, we describe an efficient numericalprocedure for computing GBPDN via a primal-dual convex optimization scheme, anddemonstrate its effectiveness through simulations.

Stabilizing Nonuniformly Quantized Compressed Sensing with Scalar Companders