Locally stationary covariance and signal estimation with macrotiles

被引:10
作者
Donoho, DL [1 ]
Mallat, S
von Sachs, R
Samuelides, Y
机构
[1] Stanford Univ, Dept Stat, Stanford, CA 94305 USA
[2] Ecole Polytech, CMAP, F-91128 Palaiseau, France
[3] Catholic Univ Louvain, Inst Stat, B-1348 Louvain, Belgium
关键词
best basis; covariance estimation; cosine basis; local stationarity; noise removal; spectrum estimation;
D O I
10.1109/TSP.2002.808116
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
A macrotile estimation algorithm is introduced to estimate the covariance of locally 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 searching for a best basis among a dictionary of orthogonal bases and by constructing an adaptive segmentation of this basis to estimate the covariance coefficients. The macrotile algorithm provides a consistent estimation of the covariance of locally stationary processes, using a dictionary of local cosine bases. This estimation is computed with a fast algorithm. Macrotile algorithms apply to other estimation problems such as the removal of additive noise in signals. This simpler problem is used as an intuitive, guide to better understand the case of covariance estimation. Examples of removal of white noise from sounds illustrate the results.
引用
收藏
页码:614 / 627
页数:14
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