An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint

@article{Daubechies2003AnIT,
  title={An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint},
  author={I. Daubechies and M. Defrise and C. D. Mol},
  journal={Communications on Pure and Applied Mathematics},
  year={2003},
  volume={57},
  pages={1413-1457}
}
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted p-penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem. Use of such p-penalized problems with p < 2 is often advocated when one expects the underlying ideal noiseless solution to have a sparse expansion with respect to the basis under… Expand
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References

SHOWING 1-10 OF 55 REFERENCES
An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections.
  • 106
Adaptive Wavelet Galerkin Methods for Linear Inverse Problems
  • 98
  • PDF
Wavelet Shrinkage: Asymptopia?
  • 1,576
  • PDF
Wavelet methods for inverting the Radon transform with noisy data
  • 64
  • PDF
Nonlinear approximation
  • 826
  • PDF
Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage
  • 770
  • PDF
...
1
2
3
4
5
...