A Flexible and Simple Lossless DWT Filter Bank Using a MAXFLAT FIR Half-Band Filter

• Published in: Applied sciences Vol. 12; no. 18; p. 9166
• Main Authors: Chung, Daewon, Cho, Woon, Kim, Yunsun, Jeon, Joonhyeon
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2022
• Subjects: Archives & records; Complexity; Computer applications; Design; Discrete Wavelet Transform; DWT filter bank; Flexibility; Image retrieval; lossless two-band filter bank; quadrature mirror filter; wavelet transform; Wavelet transforms
• ISSN: 2076-3417; 2076-3417
• DOI: 10.3390/app12189166

This paper describes a simple, lossless and computationally efficient two-band single (s-) filter bank that creates an opposite band output by subtracting the primary filtered data from the original data. For computationally efficient and error-free s-filter bank achievement, a maximally flat (MAXFLAT) half-band filter with zero odd-order coefficients is characterized from a unique perfect reconstruction condition, and an explicit impulse–response formula (for non-zero integer coefficients of even order) is derived in a closed form of the filter. The examples are shown to provide a complete and accurate solution for the design of such s-filter banks. In addition, the effectiveness of the proposed s-filter banks is clearly verified by comparing the lossless 5/3 and lossy 9/7 filter banks (in the JPEG2000). The simulation results show that the s-filter banks lead to better performance than the JPEG2000 filter banks using two filters although allowing low computational complexity of less than 50%. This new approach is shown to provide significant advantages over existing lossless discrete wavelet transform (DWT) filter banks in both design flexibility and computational complexity.