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Compressive Sensing (m15132)
Language: English
Popularity: 41.53%
Revised: 2007-09-21
Revisions: New
Null space conditions (m37170)
Keywords: Instance optimality, Null space property, Spark, Uniform guarantees
Summary: This module introduces the spark and the null space property, two common conditions related to the null space of a measurement matrix that ensure the success of sparse recovery algorithms. Furthermore, the null space property is shown to be a necessary condition for instance optimal or uniform recovery guarantees.
Subject: Mathematics and Statistics
Language: English
Popularity: 39.07%
Revised: 2011-04-14
Revisions: 6
Signal recovery via ℓ_1 minimization (m37179)
Keywords: ℓ_0 minimization, ℓ_1 minimization, Convex relaxation, Sparse recovery
Summary: This module introduces and motivates ℓ_1 minimization as a framework for sparse recovery.
Subject: Mathematics and Statistics
Language: English
Popularity: 38.48%
Revised: 2011-04-14
Revisions: 5
Complete Vector Spaces (m33548)
Keywords: Banach Spaces, Completeness, Hilbert Spaces, Vector Spaces
Subject: Mathematics and Statistics
Language: English
Popularity: 36.10%
Revised: 2010-07-16
Revisions: 2
The cross-polytope and phase transitions (m37184)
Keywords: Cross-polytope, L1 minimization, Phase transition
Summary: In this module we provide an overview of the relationship between L1 minimization and random projections of the cross-polytope.
Subject: Mathematics and Statistics
Language: English
Popularity: 35.33%
Revised: 2011-05-23
Revisions: 5
ℓ_1 minimization proof (m37187)
Keywords: ℓ_1 minimization, Sparse signal recovery
Summary: In this module we prove one of the core lemmas that is used throughout this course to establish results regarding ℓ_1 minimization.
Subject: Mathematics and Statistics
Language: English
Popularity: 34.07%
Revised: 2011-04-15
Revisions: 4
Signal recovery in noise (m37182)
Keywords: Bounded noise, Dantzig selector, Gaussian noise, L1 minimization, Signal recovery in noise, Sparse signal recovery
Summary: This module establishes a number of results concerning various L1 minimization algorithms designed for sparse signal recovery from noisy measurements. The results in this module apply to both bounded noise as well as Gaussian (or more generally, sub-Gaussian) noise.
Subject: Mathematics and Statistics
Language: English
Popularity: 33.95%
Revised: 2011-04-14
Revisions: 5
Linear Combinations of Vectors (m34030)
Subject: Science and Technology
Language: English
Popularity: 32.22%
Revised: 2010-07-16
Revisions: 2
Proof of the RIP for sub-Gaussian matrices (m37186)
Keywords: Concentration of measure, Johnson-Lindenstrauss lemma, Random matrices, Restricted isometry property, Sub-Gaussian distributions, Sub-Gaussian matrices
Summary: In this module we provide a proof that sub-Gaussian matrices satisfy the restricted isometry property.
Subject: Mathematics and Statistics
Language: English
Popularity: 31.59%
Revised: 2013-02-19
Revisions: 5
Group testing and data stream algorithms (m37362)
Keywords: Data streams, Group testing, Sketching
Summary: This module provides an overview of the relationship between compressive sensing and problems in theoretical computer science including combinatorial group testing and computation on data streams.
Subject: Mathematics and Statistics
Language: English
Popularity: 29.60%
Revised: 2011-04-15
Revisions: 4
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Total Modules: 21811