Signal and Covariance Estimation with Macrotiles

Donoho, David;Mallat, S.;von Sachs, Rainer;Samuelides, Yann
(2001) , 29 pages

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Authors
  • Donoho, DavidStanford University
    Author
  • Mallat, S.
    Author
  • von Sachs, RainerUCLouvain
    Author
  • Samuelides, Yann
    Author
Abstract
A macrotile estimation algorithm is introduced to remove additive noise from signals and to estimate the covariance of non-stationary processes. A macrotile algorithm uses a penalized method to optimize the partition of the space in orthogonal subspaces, and the estimation is computed with a projection operator. It is implemented by search- ing for a best basis among a dictionary of orthogonal bases, and by constructing an adaptive segmentation of this basis. Macrotile models are studied with local cosine bases to remove noise from sounds and to estimate the covariance matrices of locally stationary processes. The model selection and the estimation are implemented with a fast algo- rithm.
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Donoho, D., Mallat, S., von Sachs, R., & Samuelides, Y. (2001). Signal and Covariance Estimation with Macrotiles (STAT Discussion Paper 0113). https://hdl.handle.net/2078.5/88857