Compressed sensing with coherent and redundant dictionaries
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TLDR
A condition on the measurement/sensing matrix is introduced, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are nearly sparse in (possibly) highly overcomplete and coherent dictionaries.About:
This article is published in Applied and Computational Harmonic Analysis.The article was published on 2011-07-01 and is currently open access. It has received 890 citations till now. The article focuses on the topics: Restricted isometry property & Compressed sensing.read more
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Proceedings ArticleDOI
FREAK: Fast Retina Keypoint
TL;DR: This work proposes a novel keypoint descriptor inspired by the human visual system and more precisely the retina, coined Fast Retina Keypoint (FREAK), which is in general faster to compute with lower memory load and also more robust than SIFT, SURF or BRISK.
BookDOI
Compressed sensing : theory and applications
Yonina C. Eldar,Gitta Kutyniok +1 more
TL;DR: In this paper, the authors introduce the concept of second generation sparse modeling and apply it to the problem of compressed sensing of analog signals, and propose a greedy algorithm for compressed sensing with high-dimensional geometry.
Journal ArticleDOI
Discrete Signal Processing on Graphs: Sampling Theory
TL;DR: It is shown that perfect recovery is possible for graph signals bandlimited under the graph Fourier transform and the connection to the sampling theory of finite discrete-time signal processing and previous work on signal recovery on graphs is established.
Journal ArticleDOI
Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model
TL;DR: This paper presents an alternative, analysis-based model, where an analysis operator-hereafter referred to as the analysis dictionary-multiplies the signal, leading to a sparse outcome.
Journal ArticleDOI
Spectral compressive sensing
TL;DR: The spectral CS (SCS) recovery framework for arbitrary frequencysparse signals is introduced and it is demonstrated that SCS signicantly outperforms current state-of-the-art CS algorithms based on the DFT while providing provable bounds on the number of measurements required for stable recovery.
References
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Journal ArticleDOI
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Journal ArticleDOI
Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
Journal ArticleDOI
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: It is demonstrated theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal.