Image processing technique using band splitting in the Fresnel transformed signal domain
Satoshi Ito, Yoshifumi Yamada · Systems and Computers in Japan · 2003
Abstract There are two methods for solving the Fresnel transform formula using Fourier transforms, one of which uses the Fourier transform once and the other uses it twice. When Fresnel transformed signal of an image is calculated using the inverse algorithm of the latter Fresnel transform method and then the Fresnel transform is calculated by the former Fresnel transform method, the image can be scaled by an arbitrary rate. When the image is down scaled, an alias signal produced in the calculation of the discrete Fresnel transform appears as edge component of the image having high‐frequency components of the original image. The images corresponding to each hand of the Fresnel transformed signal are reconstructed in a different region of the reconstructed image domain like the wavelet‐based multiresolution image analysis. In this paper, the authors describe the band splitting effect due to the Fresnel transforms and compare its characteristics with those of a wavelet image analysis. Also, as an image processing application, the authors performed image sharpening processing for enhancing the signal of the high‐frequency region while suppressing noise. The results confirmed that favorable effects are obtained which are similar to those obtained for wavelets. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(8): 51–61, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/scj.10290