Integration-free projection of a sampled signal on a multiresolution analysis ladder space via approximation theory

Dumitru Mihai Ionescu; Mark A. Wickert; Jacqueline J. Hine

doi:10.1117/12.255229

23 October 1996 Integration-free projection of a sampled signal on a multiresolution analysis ladder space via approximation theory

Dumitru Mihai Ionescu, Mark A. Wickert, Jacqueline J. Hine

Author Affiliations +

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255229
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

Let H^s be the Sobolev space of exponent s >= 0. Let V_i, i (epsilon) Z,...V_i is contained in V_i-1 is contained in ..., be the ladder spaces of a multiresolution analysis (MRA) in L²(R) associated with a compactly supported scaling function (phi) (epsilon) H^(sigma ) which verifies supp(phi) equals [ 0, L-1 ], L (epsilon) N, (sigma) > 1/2. Let f (epsilon) L²(R) be compactly supported with countable many discontinuity points and verifying suppf equals [ t₁, t₂ ], where 0 < (mu) (suppf) < (infinity) and, for i equals 1,2 and some integer m$_0), t_i equals n_i(m₀)2^mo with n_i(m₀) (epsilon) Z. The goal is to approximate f by a function in V_m which approaches f in some sense as the scale becomes finer, reproduces the values of f at certain equally spaced, arbitrarily close points and is not necessarily the orthogonal projection of f on V_m. Such non-orthogonal projections can be used to start the pyramid algorithm or to approximate f, as an alternative which is better than using the samples themselves in place of the true inner products and faster than integrating for the inner products. The almost uniform convergence feature allows interactive control on the selection of an initial sampling rate that is capable of preserving details down to a desired resolution.

Citation Download Citation

Dumitru Mihai Ionescu, Mark A. Wickert, and Jacqueline J. Hine "Integration-free projection of a sampled signal on a multiresolution analysis ladder space via approximation theory", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255229

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available