Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
2007/12/01 by Joel A. Tropp, Anna C. Gilbert · 9,713 citations
Computer Science · Engineering · Mathematics · #Algorithm #Basis pursuit #Blind Source Separation Techniques #Combinatorics #Compressed sensing #Computer science #Dimension (graph theory) #Emphasis (telecommunications) #Greedy algorithm #Matching (statistics) #Matching pursuit #Mathematics #Microwave Imaging and Scattering Analysis #SIGNAL (programming language) #Signal processing #Signal reconstruction #Sparse and Compressive Sensing Techniques #Statistics #Telecommunications
paper · doi:10.1109/tit.2007.909108
published in IEEE Transactions on Information Theory 53(12), 4655-4666 (Institute of Electrical and Electronics Engineers)
openalex publication_date 2007/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
This paper demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal withmnonzero entries in dimensiondgiven \rm O(m ln d)random linear measurements of that signal. This is a massive improvement over previous results, which require\rm O(m2)measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems.
Citations
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- When machine vision meets histology: A comparative evaluation of model architecture for classification of histology sections. [europepmc]
- A Novel Partial Discharge Localization Method in Substation Based on a Wireless UHF Sensor Array. [europepmc]
- Electrocardiograph signal denoising based on sparse decomposition. [europepmc]
- Dictionary learning-based reverberation removal enables depth-resolved photoacoustic microscopy of cortical microvasculature in the mouse brain. [europepmc]
- Infrared Image Super Resolution by Combining Compressive Sensing and Deep Learning. [europepmc]
- A super-resolution method-based pipeline for fundus fluorescein angiography imaging. [europepmc]
- A Regularized Weighted Smoothed L ₀ Norm Minimization Method for Underdetermined Blind Source Separation. [europepmc]
- A Comprehensive Survey on Spectrum Sensing in Cognitive Radio Networks: Recent Advances, New Challenges, and Future Research Directions. [europepmc]
- Enhanced Cerenkov luminescence tomography analysis based on Y 2 O 3 :Eu 3+ rare earth oxide nanoparticles. [europepmc]
- Bayesian Compress Sensing Based Countermeasure Scheme Against the Interrupted Sampling Repeater Jamming. [europepmc]
- Compressive Sensing Inference of Neuronal Network Connectivity in Balanced Neuronal Dynamics. [europepmc]
- A Perspective on MR Fingerprinting. [europepmc]
- Combining Denoising Autoencoders and Dynamic Programming for Acoustic Detection and Tracking of Underwater Moving Targets. [europepmc]
- Manifold learning based data-driven modeling for soft biological tissues. [europepmc]
- 3-D compressed sensing optical coherence tomography using predictive coding. [europepmc]
- Compressed Sensing of Extracellular Neurophysiology Signals: A Review. [europepmc]
- Discovery of nonlinear dynamical systems using a Runge-Kutta inspired dictionary-based sparse regression approach. [europepmc]
- Deep Compressive Sensing on ECG Signals with Modified Inception Block and LSTM. [europepmc]
- Motion-compensated T 1 mapping in cardiovascular magnetic resonance imaging: a technical review. [europepmc]
- A compressive hyperspectral video imaging system using a single-pixel detector. [europepmc]
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