M. Fornasier

Publications117
h-index34
Citations5,860
Highly Influential Citations389
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Iteratively reweighted least squares minimization for sparse recovery
Under certain conditions (known as the restricted isometry property, or RIP) on the mN matrix ˆ (where m<N ), vectors x 2 R N that are sparse (i.e., have most of their entries equal to 0) can be… Expand
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Compressive Sensing
TLDR
Compressive sensing is a new type of sampling theory, which predicts that sparse signals and images can be reconstructed from what was previously believed to be incomplete information. Expand
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Compressive Sensing and Structured Random Matrices
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Theoretical Foundations and Numerical Methods for Sparse Recovery
  • M. Fornasier
  • Computer Science
  • Radon Series on Computational and Applied…
  • 16 January 2010
TLDR
The present collection of four lecture notes is the very first contribution of this type in the field of sparse recovery and may serve as a textbook for graduate courses. Expand
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Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints
Regularization of ill-posed linear inverse problems via ℓ1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an ℓ1… Expand
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Low-rank Matrix Recovery via Iteratively Reweighted Least Squares Minimization
TLDR
We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements with an error of the order of the best $k$-rank approximation. Expand
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Continuous Frames, Function Spaces, and the Discretization Problem
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain… Expand
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Iteratively Re-weighted Least Squares minimization: Proof of faster than linear rate for sparse recovery
TLDR
We show that if there is a sparse solution, the limit of the proposed algorithm is that sparse solution. Expand
  • 109
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Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
TLDR
We show how to compute solutions of linear inverse problems with joint sparsity regularization constraints by fast thresholded Landweber algorithms. Expand
  • 229
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Intrinsic Localization of Frames
AbstractSeveral concepts for the localization of a frame are studied. The intrinsic localization of a frame is defined by the decay properties of its Gramian matrix. Our main result asserts that the… Expand
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