Practical Signal Recovery from Random Projections

By Justin K. Romberg. 2005

367 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b06117267cbdc643a36d9581352bf893f1f0566b

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Citations in the corpus

Block Compressed Sensing of Natural Images (2007, methodology): “It should also be emphasized that our algorithms are much simpler than those in [6] both at the sender and the reconstruction sides.”
Compressive sensing: From theory to applications, a survey (2013, methodology): “…as where Similarly, by using l 1 minimization or BP, as it is known in CS literature, signal can be exactly recovered from ‘ m ’ measurements by solving a simple convex optimization problem [21] through linear programming. where Some reconstruction techniques are based on l 0 minimization.”
Learning Sparsifying Transforms (2013, background): “The transform model Wy ≈ x with x sparse, is also more general than the notion of compressibility [46] applied to Wy, where the assumption would be that the coefficients of Wy, when arranged in non-increasing magnitude order, follow a power law decay.”
Iterative Thresholding for Sparse Approximations (2008, methodology): “In some applications, such as compressive sampling [20], it is desirable to exactly recover the elements used to construct the observation x.”
Highly Undersampled Magnetic Resonance Image Reconstruction via Homotopic $\ell_{0}$ -Minimization (2009, background): “In practice, the requisite degree of oversampling necessary to achieve exact reconstruction of a signal of car dinality S is roughly 3S − 5S [9], where the multiplicative constant is proportional to the restricted isometry consta nt for a givenΦ.”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, unknown): “Candès and Romberg [14] have developed a fast approximate `1 solver using projections onto convex sets.”
Compressive Sensing via Nonlocal Low-Rank Regularization (2014, methodology): “In the first experiment, we generate CS measurements by randomly sampling the Fourier transform coefficients of input images [30], [31].”
Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing (2009, methodology): “For example the use of total variation (TV) [27] is generally a non-statistical approach that may be employed to account for prior knowledge about the properties of images.”
Wave atoms and sparsity of oscillatory patterns (2007, background): “ical principles; where higher-level adaptive transform (like wedgeprints [35] or bandelets [28]) can even be defined on top of wavelets; and where nonlinear recovery techniques can exploit sparsity in the wavelet domain [32, 18, 10].”
Sampling Theorems for Signals From the Union of Finite-Dimensional Linear Subspaces (2009, background): “For example, it is not only required that two distinct signals are mapped to distinct observations, it is also important that the distance between distinct signals is not changed too much in the observation domain [6], [10], [16], [32], [16].”
Compressed Sensing MRI (2008, background): “In fact, iterative algorithms for solving such formal optimization problems in effect perform thresholding and interference cancellation at each iteration so there is a close connection between our exposition and more formal approaches [41], [50], [52], [53].”
Templates for convex cone problems with applications to sparse signal recovery (2010, background): “4) is to look for a sparse object in a transformed domain while reducing artifacts due to sparsity constraints alone, such as Gibbs oscillations, by means of the total-variation norm [12,15,59].”
DART: A Practical Reconstruction Algorithm for Discrete Tomography (2011, unknown): “total variation minimization [8], [10], [28].”
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science (2010, methodology): “The constrained l1 minimization model aims to recover a sparse signal in the wavelet domain that is consistent with these partial DCT measurements [8].”