Recursive Orthgonal Wavelet Function

Research Project

Project/Area Number	05650359
Research Category	Grant-in-Aid for General Scientific Research (C)
Allocation Type	Single-year Grants
Research Field	情報通信工学
Research Institution	Keio University
Principal Investigator	TAKAHASHI Shinichi Keio Univ.Elec.Eng.Prof., 理工学部, 教授 (50051561)
Co-Investigator(Kenkyū-buntansha)	IKEHARA Masaaki Keio Univ.Elec.Eng.Assist.Prof., 理工学部, 専任講師 (00212796) HAMADA Nozomu Keio Univ.Elec.Eng.Prof., 理工学部, 教授 (80051902)
Project Period (FY)	1993 – 1994
Project Status	Completed (Fiscal Year 1994)
Budget Amount *help	¥2,100,000 (Direct Cost: ¥2,100,000) Fiscal Year 1994: ¥400,000 (Direct Cost: ¥400,000) Fiscal Year 1993: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywords	Wavelet Transform / Digital signal Processing / Recursive Filters / ウェーブレット変換 / ウエーブレット変換
Research Abstract	In this research, we propose a design method of 1 and 2 dimensional recursive wavelet functions and examine its applications for digital signal processing. In this method, we use the parallel connection consisted of some delays and 1 and 2-D allpass filter in order to satisfy the orthogonality. Furthemore a maximum number of zeros is put at aliasing frequencies in the lowpass filter to obtain the regularity. IIR transfer function with some degrees of regularity and arbitrary order can be easily obtained by solving the simultaneous equation. 1-D and 2-D recursive wavelet functions based on iterated filter banks are found. Although the obtained wavelet functions are similar to that based on FIR filters, recursive wavelet functions have higher regularity than nonrecursive wavelet. Next, we considered its application for digital signal processing, singularity detection and image compression. In image ompression, image is separated into multiresolution spaces by wavelet transform. Each multiresolution spaces is coded by using IFS (Iterated Function System) . In this time, IFS codes are make based on the characteristics of each spaces. By this method, good reconstruction image can be obtained.