A generalization of restricted isometry property and applications to compressed sensing
نویسنده
چکیده
This paper introduces a new general theory of compressed sensing. We give a natural generalization of the restricted isometry property (RIP) called weak RIP. We consider the proposed theory to be more useful for real data analysis than the RIP. In this note, we verify the accuracy of the weak RIP by showing in reconstruction from undersampling measurements where it is possible to improve estimation in various situations.
منابع مشابه
A Weak RIP of theory of compressed sensing and LASSO
This paper introduce simple and general theories of compressed sensing and LASSO. The novelty is that our recovery results do not require the restricted isometry property(RIP). We use the notion of weak RIP that is a natural generalization of RIP. We consider that the proposed results are more useful and flexible for real data analysis in various fields.
متن کاملAn RIP-based approach to $\Sigma\Delta$ quantization for compressed sensing
In this paper, we provide a new approach to estimating the error of reconstruction from Σ∆ quantized compressed sensing measurements. Our method is based on the restricted isometry property (RIP) of a certain projection of the measurement matrix. Our result yields simple proofs and a slight generalization of the best-known reconstruction error bounds for Gaussian and subgaussian measurement mat...
متن کاملA remark on weaken restricted isometry property in compressed sensing
The restricted isometry property (RIP) has become well-known in the compressed sensing community. Recently, a weaken version of RIP was proposed for exact sparse recovery under weak moment assumptions. In this note, we prove that the weaken RIP is also sufficient for stable and robust sparse recovery by linking it with a recently introduced robust width property in compressed sensing. Moreover,...
متن کاملOn the absence of the RIP in real-world applications of compressed sensing and the RIP in levels
The purpose of this paper is twofold. The first is to point out that the Restricted Isometry Property (RIP) does not hold in many applications where compressed sensing is successfully used. This includes fields like Magnetic Resonance Imaging (MRI), Computerized Tomography, Electron Microscopy, Radio Interferometry and Fluorescence Microscopy. We demonstrate that for natural compressed sensing ...
متن کاملA Compressed Introduction to Compressed Sensing
We attempt to convey a sense of compressed sensing. Specifically, we discuss how `1 minimization and the restricted isometry property for matrices can be used for sparse recovery of underdetermined linear systems even in the presence of noise.
متن کامل