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 fields of compressed sensing (CS) and matrix completion have shown thathigh-dimensional signals with sparse or low-rank structure can be effectivelyprojected into a low-dimensional space (for efficient acquisition orprocessing) when the projection operator achieves a stable embedding of thedata by satisfying the Restricted Isometry Property (RIP). It has also beenshown that such stable embeddings can be achieved for general Riemanniansubmanifolds when random orthoprojectors are used for dimensionality reduction.Due to computational costs and system constraints, the CS community hasrecently explored the RIP for structured random matrices (e.g., randomconvolutions, localized measurements, deterministic constructions). The maincontribution of this paper is to show that any matrix satisfying the RIP (i.e.,providing a stable embedding for sparse signals) can be used to construct astable embedding for manifold-modeled signals by randomizing the column signsand paying reasonable additional factors in the number of measurements. Wedemonstrate this result with several new constructions for stable manifoldembeddings using structured matrices. This result allows advances in efficientprojection schemes for sparse signals to be immediately applied to manifoldsignal models.

Stable Manifold Embeddings with Structured Random Matrices