Efficient Rationalization of Triplet Halfband Filter Banks and its Application to Image Compression

This paper presents a novel approach for rationalization of irrational coefficients of filters designed using three-step lifting scheme. The existing three-step lifting schemes result in the irrational filter coefficients which require infinite precision for implementation. In this work, Euler-Frobenius halfband polynomials are designed to obtain the required kernels of three-step lifting structure. Next, the efficient rationalization of the designed filter banks (FBs) is proposed to reduce the arithmetic complexity. The proposed rational FBs preserve perfect reconstruction, near-orthogonality and regularity properties of wavelet FBs. These filters with rational coefficients are then used in image compression algorithms to compress the test images in well-known Classic, EPFL, RAISE, FiveK datasets and chromosome image datasets. The performance of the proposed rational FBs is compared with the existing rational FBs. It is observed that the performance of the proposed rational FBs is improved in terms of computational cost, encoding-decoding time and compression ratio as compared to existing rational FBs.