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

We introduce a new ensemble of random bipartite graphs, which we term the`smearing ensemble', where each left node is connected to some number ofconsecutive right nodes. Such graphs arise naturally in the recovery of sparsewavelet coefficients when signal acquisition is in the Fourier domain, such asin magnetic resonance imaging (MRI). Graphs from this ensemble exhibit small,structured cycles with high probability, rendering current techniques fordetermining iterative decoding thresholds inapplicable. In this paper, wedevelop a theoretical platform to analyze and evaluate the effects ofsmearing-based structure. Despite the existence of these small cycles, wederive exact density evolution recurrences for iterative decoding on graphswith smear-length two. Further, we give lower bounds on the performance of amuch larger class from the smearing ensemble, and provide numerical experimentsshowing tight agreement between empirical thresholds and those determined byour bounds. Finally, we describe a system architecture to recover sparsewavelet representations in the MRI setting, giving explicit thresholds on theminimum number of Fourier samples needing to be acquired for the $1$-stage Haarwavelet setting. In particular, we show that $K$-sparse $1$-stage Haar waveletcoefficients of an $n$-dimensional signal can be recovered using $2.63K$Fourier domain samples asymptotically using $\mathcal{O}(K\log{K})$ operations.

Density Evolution on a Class of Smeared Random Graphs: A Theoretical Framework for Fast MRI