Generalized notions of sparsity and restricted isometry property. Part II: Applications
The restricted isometry property (RIP) is a universal tool for data recovery. We explore the implication of the RIP in the framework of generalized sparsity and group measurements introduced in the Part I paper. It turns out that for a given measurement instrument the number of measurements for RIP can be improved by optimizing over families of Banach spaces. Second, we investigate the preservation of difference of two sparse vectors, which is not trivial in generalized models. Third, we extend the RIP of partial Fourier measurements at optimal scaling of number of measurements with random sign to far more general group structured measurements. Lastly, we also obtain RIP in infinite dimension in the context of Fourier measurement concepts with sparsity naturally replaced by smoothness assumptions.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Generalized notions of sparsity and restricted isometry property. Part I: A unified framework
The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank te…
compressed sensingDimensionality ReductionNear-Ideal Behavior of Compressed Sensing Algorithms
In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose $y = Az + \eta$ where $A$ satisfies the restricted isometry property (RIP) with a sufficiently small…
compressed sensingRestricted Isometry Property of Gaussian Random Projection for Finite Set of Subspaces
Dimension reduction plays an essential role when decreasing the complexity of solving large-scale problems. The well-known Johnson-Lindenstrauss (JL) Lemma and Restricted Isometry Property (RIP) admit the use of random p…
Clusteringcompressed sensingDimensionality ReductionLEMMAA theory of optimal convex regularization for low-dimensional recovery
We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constra…
RIPML: A Restricted Isometry Property based Approach to Multilabel Learning
The multilabel learning problem with large number of labels, features, and data-points has generated a tremendous interest recently. A recurring theme of these problems is that only a few labels are active in any given d…
Dimensionality Reduction