Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#287183] of Ingrid Daubechies

Papers Published

  1. Daubechies, I; Fornasier, M; Loris, I, Accelerated projected gradient method for linear inverse problems with sparsity constraints, Journal of Fourier Analysis and Applications, vol. 14 no. 5-6 (2008), pp. 764-792, ISSN 1069-5869 [doi]
    (last updated on 2017/12/12)

    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 penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to ℓ1-constraints, using a gradient method, with projection on ℓ1-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration. © 2008 Birkhäuser Boston.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320