The optimal reconstruction from blurred and nonuniformly sampled data based on the optimum discrete approximation minimizing various worst-case measures of error

Yuichi Kida; Takuro Kida

doi:10.1117/12.680413

5 September 2006 The optimal reconstruction from blurred and nonuniformly sampled data based on the optimum discrete approximation minimizing various worst-case measures of error

Yuichi Kida, Takuro Kida

Author Affiliations +

Proceedings Volume 6316, Image Reconstruction from Incomplete Data IV; 63160A (2006) https://doi.org/10.1117/12.680413
Event: SPIE Optics + Photonics, 2006, San Diego, California, United States

Abstract

Extended interpolatory approximation is discussed for some classes of n-dimensional vector signals. Firstly, we present two sufficient conditions of the optimum approximation and prove that the proposed optimum approximation using fixed finite number of sample values satisfies these two conditions. Secondly, we discuss the optimum running approximation of n-dimensional time-limited vector signals based on a certain one-to-one correspondence between a vector signal and the corresponding vector error signal of approximation. The proposed optimum approximation has the minimum measure of error among almost all the linear and the nonlinear approximations using the same measure of error and generalized sample values. Note that the proposed optimum approximation can be realized by flexible FIR filter bank. The term "flexible" means that we can widely choose the number of paths and frequency response of time-invariant FIR analysis filters. Moreover, we can use sample points that are distributed on an arbitrary periodical pattern.

Citation Download Citation

Yuichi Kida and Takuro Kida "The optimal reconstruction from blurred and nonuniformly sampled data based on the optimum discrete approximation minimizing various worst-case measures of error", Proc. SPIE 6316, Image Reconstruction from Incomplete Data IV, 63160A (5 September 2006); https://doi.org/10.1117/12.680413

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