Share This Author
Atomic Decomposition by Basis Pursuit
Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Ideal spatial adaptation by wavelet shrinkage
SUMMARY With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline,…
De-noising by soft-thresholding
- D. Donoho
- Computer ScienceIEEE Trans. Inf. Theory
- 1 May 1995
The authors prove two results about this type of estimator that are unprecedented in several ways: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures.
Sparse MRI: The application of compressed sensing for rapid MR imaging
Practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference and demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin‐echo brain imaging and 3D contrast enhanced angiography.
Adapting to Unknown Smoothness via Wavelet Shrinkage
Abstract We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet…
Message-passing algorithms for compressed sensing
- D. Donoho, A. Maleki, A. Montanari
- Computer ScienceProceedings of the National Academy of Sciences
- 21 July 2009
A simple costless modification to iterative thresholding is introduced making the sparsity–undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures, inspired by belief propagation in graphical models.
Fast Discrete Curvelet Transforms
- E. Candès, L. Demanet, D. Donoho, Lexing Ying
- Computer ScienceMultiscale Model. Simul.
- 26 September 2006
This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform in two and three dimensions, based on unequally spaced fast Fourier transforms, while the second is based on the wrapping of specially selected Fourier samples.
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization
- D. Donoho, Michael Elad
- Computer ScienceProceedings of the National Academy of Sciences…
- 21 February 2003
This article obtains parallel results in a more general setting, where the dictionary D can arise from two or several bases, frames, or even less structured systems, and sketches three applications: separating linear features from planar ones in 3D data, noncooperative multiuser encoding, and identification of over-complete independent component models.
Higher criticism for detecting sparse heterogeneous mixtures
Higher criticism, or second-level significance testing, is a multiplecomparisons concept mentioned in passing by Tukey. It concerns a situation where there are many independent tests of significance…