Unconditional bases are optimal bases for data compression and for statistical estimation

Unconditional bases are optimal bases for data compression and for statistical estimation (1993)

by David L. Donoho

Venue:	Applied and Computational Harmonic Analysis
Citations:	122 - 23 self

Datum	Value	Source
TITLE	Unconditional bases are optimal bases for data compression and for statistical estimation	INFERENCE
AUTHOR NAME	David L. Donoho	SVM HeaderParse 0.2
AUTHOR AFFIL	Department of Statistics; Stanford University	SVM HeaderParse 0.2
ABSTRACT	An orthogonal basis of L 2 which is also an unconditional basis of a functional space F is a kind of optimal basis for compressing, estimating, and recovering functions in F. Simple thresholding operations, applied in the unconditional basis, work essentially better for compressing, estimating, and recovering than they do in any other orthogonal basis. In fact, simple thresholding in an unconditional basis works essentially better for recovery and estimation than other methods, period. (Performance is measured in an asymptotic minimax sense.) As an application, we formalize and prove Mallat's Heuristic, which says that wavelet bases are optimal for representing functions containing singularities, when there may be an arbitrary number of singularities, arbitrarily distributed.	SVM HeaderParse 0.2
YEAR	1993	INFERENCE
VENUE	Applied and Computational Harmonic Analysis	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	100--115	INFERENCE
CITATIONS	34 found	ParsCit 1.0