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

Solving quadratic systems of equations in n variables and m measurements ofthe form $y_i = |a^T_i x|^2$ , $i = 1, ..., m$ and $x \in R^n$ , which is alsoknown as phase retrieval, is a hard nonconvex problem. In the case of standardGaussian measurement vectors, the wirtinger flow algorithm Chen and Candes(2015) is an efficient solution. In this paper, we proposed a new form ofwirtinger flow and a new spectral initialization method based on this newalgorithm. We proved that the new wirtinger flow and initialization methodachieve linear sample and computational complexities. We further extended thenew phasing algorithm by combining it with other existing methods. Finally, wedemonstrated the effectiveness of our new method in the low data to parameterratio settings where the number of measurements which is less thaninformation-theoretic limit, namely, $m < 2n$, via numerical tests. Forinstance, our method can solve the quadratic systems of equations with gaussianmeasurement vector with probability $\ge 97\%$ when $m/n = 1.7$ and $n = 1000$,and with probability $\approx 60\%$ when $m/n = 1.5$ and $n = 1000$.

Solving Random Systems of Quadratic Equations with Tanh Wirtinger Flow