Phase Transitions for Restricted Isometry Properties
نویسندگان
چکیده
Currently there is no framework for the transparent comparison of sparse approximation recoverability results derived using different methods of analysis. We cast some of the most recent recoverability results for `1-regularization in terms of the phase transition framework advocated by Donoho. To allow for quantitative comparisons across different methods of analysis a particular random matrix ensemble must be selected; here we focus on Gaussian random matrices. Methods of analysis considered include the Restricted Isometry Property of Candès and Tao, geometric covering arguments of Rudelson and Vershynin, and convex polytopes formulations of Donoho.
منابع مشابه
On Support Sizes of Restricted Isometry Constants
A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao. For qualitative comparison of sufficient conditions derived from an RIP analysis, the support size of the RIP constants is generally reduced as much as possible with the goal of achieving a support size of twice the sparsity of the target signal. Using a quantitat...
متن کاملMagnetic Properties and Phase Transitions in a Spin-1 Random Transverse Ising Model on Simple Cubic Lattice
Within the effective-field theory with correlations (EFT), a transverse random field spin-1 Ising model on the simple cubic (z=6) lattice is studied. The phase diagrams, the behavior of critical points, transverse magnetization, internal energy, magnetic specific heat are obtained numerically and discussed for different values of p the concentration of the random transverse field.
متن کاملQuasi-linear Compressed Sensing
Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are quasi-linear. We formulate natural generalizations of the well-known Restricted Isometry Property (RIP) towards nonlinear measurements, which allow us to prove bot...
متن کاملRestricted isometry properties and nonconvex compressive sensing
In previous work, numerical experiments showed that ` minimization with 0 < p < 1 recovers sparse signals from fewer linear measurements than does ` minimization. It was also shown that a weaker restricted isometry property is sufficient to guarantee perfect recovery in the ` case. In this work, we generalize this result to an ` variant of the restricted isometry property, and then determine ho...
متن کاملBounds on restricted isometry constants of random matrices
In this paper we look at isometry properties of random matrices. During the last decade these properties gained a lot attention in a field called compressed sensing in first place due to their initial use in [7, 8]. Namely, in [7, 8] these quantities were used as a critical tool in providing a rigorous analysis of l1 optimization’s ability to solve an under-determined system of linear equations...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009