Quaternion Gaussian matrices satisfy the RIP
Agnieszka Bade\'nska, {\L}ukasz B{\l}aszczyk
TL;DR
This paper proves that quaternion Gaussian random matrices satisfy the restricted isometry property with high probability, highlighting limitations of the restricted isometry random variables approach for analyzing these matrices.
Contribution
It establishes the RIP for quaternion Gaussian matrices and discusses the inappropriateness of the RIV approach for their analysis.
Findings
Quaternion Gaussian matrices satisfy RIP with overwhelming probability.
RIV approach is not suitable for analyzing quaternion Gaussian matrices.
Provides theoretical foundation for compressed sensing with quaternion matrices.
Abstract
We prove that quaternion Gaussian random matrices satisfy the restricted isometry property (RIP) with overwhelming probability. We also explain why the restricted isometry random variables (RIV) approach is not appropriate for drawing conclusions on restricted isometry constants.
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Topological and Geometric Data Analysis · Mathematical Analysis and Transform Methods