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The lifting scheme is an efficient tool to construct ```mage compression standard JPEG-2000. Daubechies wavelets can provide better image coding performance than discrete cosine transform (DCT) which is used in JPEG because the wavelets can present signal more efficiently than DCT. However, for high compression rate, the details of the decompressed images in JPEG-2000 are degraded. | Science & Technology Development, Vol 11, No.09 - 2008 OPTIMAL LIFTING WAVELET FILTER BANK DESIGN AND IMAGE COMPRESSION APPLICATION Hoang Dinh Chien University of Technolog, VNU-HCM (Manuscript Received on March 06th, 2008, Manuscript Revised May 06th, 2008) ABSTRACT: The lifting scheme is an efficient tool to construct second-generation wavelets. It has been used to realize Daubechies wavelet transform in image compression standard JPEG-2000. Daubechies wavelets can provide better image coding performance than discrete cosine transform (DCT) which is used in JPEG because the wavelets can present signal more efficiently than DCT. However, for high compression rate, the details of the decompressed images in JPEG-2000 are degraded. The reason is that Daubechies filters are maximally flat while their frequency selectivity is very poor. In this paper, we present an efficient method for the optimal design of filter banks and wavelets based on the lifting structure. The design problem is expressed as an optimization problem where the frequency selectivity of filters is optimized for a given regularity order. The simulation results show that the filter banks designed by our proposed method can offer the coding performance improvement compared to Daubechies filters in JPEG-2000. Keywords: Filter banks, wavelets, image coding, regularity, frequency selectivity, global optimization. 1.INTRODUCTION The discrete wavelet transform (DWT) has found in various signal processing applications, for example signal compression, denoising , watermarking, and so on, due to the fact that DWT can overcome the limitation of the traditional Fourier transform in being able to providing variable time and frequency resolutions [1]-[3]. As a result, the DWT has been adopted in international multimedia compression standards such as JPEG-2000 and MPEG4 [3], [4]. In the DWT based applications, proper choice of wavelets is critical to achieve systems with good performance. It is well-known that
