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.

This paper addresses the construction of a family of wavelets based on halfband polynomials. An algorithm is proposed that ensures maximum zeros at ω = π for a desired length of analysis and synthesis filters. We start with the coefficients of the polynomial (x+1)(n) and then use a generalized matrix formulation method to construct the filter halfband polynomial. The designed wavelets are efficient and give acceptable levels of peak signal-to-noise ratio when used for image compression. Furthermore, these wavelets give satisfactory recognition rates when used for feature extraction. Simulation results show that the designed wavelets are effective and more efficient than the existing standard wavelets.