New Approach to the Design of Low Complexity 9/7 Tap Wavelet Filters With Maximum Vanishing Moments

Abstract

In this paper, we present a novel approach for the design of 9/7 near-perfect-reconstruction wavelets that are efficient for image compression. These wavelets have maximum vanishing moments for both decomposition and reconstruction filters. Among the existing 9/7 tap wavelet filters, the Cohen-Daubechies-Feauveau (CDF) 9/7 are known to have the largest regularity. However, these wavelets have irrational coefficients thus requiring infinite precision implementation. Unlike state- of-art designs that compromise vanishing moments for attaining low-complexity coefficients, our algorithm ensures both. We start with a spline function of length 5 and select the remaining factors to obtain wavelets with rationalized coefficients. By proper choice of design parameters, it is possible to find very low complexity dyadic wavelets with compact support.We suggest a near half band criterion to attain a suitable combination of low-pass analysis and decomposition filters. The designed filter bank is found to give significant hardware advantage as compared with existing filter pairs. Moreover, these low-complexity wavelets have characteristics similar to standard (CDF 9/7) wavelets. The designed wavelets are tested for their suitability in applications such as image compression. Simulations results depict that the designed wavelets give comparable performances on most of the benchmark images. Subsequently, they can be used in applications that require fewer computations and lesser hardware.

A new discrete wavelet transform appropriate for hardware implementation

“…Nearly linear phase response of the filter in Symlet wavelet is used to avoid phase distortion in the under process signal. The excellent features of the existing wavelets are achieved if their irrational numbers coefficients are implemented with high precision that entails using complex hardware and much computing time . Meanwhile, there is a limited work on optimization of hardware implementation of these functions, while it is essential because of its large number of mathematical operations .…”

“…The excellent features of the existing wavelets are achieved if their irrational numbers coefficients are implemented with high precision that entails using complex hardware and much computing time. 16 Meanwhile, there is a limited work on optimization of hardware implementation of these functions, while it is essential because of its large number of mathematical operations. 17 The lifting scheme (LS) technique can reduce the number of arithmetic operations (add and multiplication operations) for realization of discrete wavelet transform (DWT) to some extent, 18,19 but this technique is more effective for lowering the number of adder blocks rather than multiplier blocks.…”

“…In Pan and Park, detail and approximation coefficients are calculated just by low‐pass filter architecture instead of both low‐pass and high‐pass filter architectures by using the symmetric relationship between the low‐pass and high‐pass filters coefficients. In Naik and Holambe, a new approach to the design of 9/7 wavelet with maximum vanishing moment is introduced in which the dyadic/integer coefficients are used to lower the hardware complexity. However, it still needs multipliers, and the computational bits of its hardware are significantly larger than those of existing wavelets.…”