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

The Compressive Sensing (CS) framework aims to ease the burden onanalog-to-digital converters (ADCs) by reducing the sampling rate required toacquire and stably recover sparse signals. Practical ADCs not only sample butalso quantize each measurement to a finite number of bits; moreover, there isan inverse relationship between the achievable sampling rate and the bit depth.In this paper, we investigate an alternative CS approach that shifts theemphasis from the sampling rate to the number of bits per measurement. Inparticular, we explore the extreme case of 1-bit CS measurements, which capturejust their sign. Our results come in two flavors. First, we consider idealreconstruction from noiseless 1-bit measurements and provide a lower bound onthe best achievable reconstruction error. We also demonstrate that i.i.d.random Gaussian matrices describe measurement mappings achieving, withoverwhelming probability, nearly optimal error decay. Next, we considerreconstruction robustness to measurement errors and noise and introduce theBinary $\epsilon$-Stable Embedding (B$\epsilon$SE) property, whichcharacterizes the robustness measurement process to sign changes. We show thesame class of matrices that provide almost optimal noiseless performance alsoenable such a robust mapping. On the practical side, we introduce the BinaryIterative Hard Thresholding (BIHT) algorithm for signal reconstruction from1-bit measurements that offers state-of-the-art performance.

Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors