A new structure of spline wavelet transform based on adaptive directional lifting for efficient image coding
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ORIGINAL PAPER
A new structure of spline wavelet transform based on adaptive directional lifting for efficient image coding Rania Boujelbene1 · Yousra Ben Jemaa1 Received: 29 December 2019 / Revised: 2 March 2020 / Accepted: 30 March 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract We present in this paper a modified structure of a polynomial spline wavelet transform based on adaptive directional lifting for image compression. The proposed method not only uses the polynomial splines as a tool for the construction of the appropriate filters seeing its efficiency as compared to other filters like the biorthogonal 9/7, but also adapts far better to the image-orientation features by carrying out a lifting-based prediction in local windows in the direction of high pixel correlation. The main purpose of this article is then to integrate the coefficients calculated by the best spline filter order into the adaptive directional lifting. The new method is designed to further reduce the magnitude of the high-frequency wavelet coefficients and preserve the detailed information of the original images more effectively. The numerical results demonstrate the efficiency of the proposed approach over the traditional lifting-based spline wavelet transform and the adaptive directional lifting with respect to both objective and subjective criteria for image compression applications. Keywords Image compression · Wavelet transform · Spline · Directional lifting
1 Introduction Despite the fact that the lifting scheme is very efficient in representing horizontal and vertical edges, this kind of lifting structure fails to provide an efficient representation for edges and textures, which are not aligned along these two directions (horizontal and vertical). Actually, natural images frequently include significant direction information which can be generally approximated as linear edges on a local level. These edges may be neither horizontal nor vertical. If not considered into account, such a fact will bring in a large magnitude in these high-frequency coefficients. A close attention has been paid to this problem not only by numerous image compression researchers [1–9], but also by many other experts in the image-processing area involving feature extraction, classification enhancement and denoising [10,11]. A lot of new geometric wavelet transforms such as contourlets [12] and curvelets [13] have been proposed to supply sparse representations of the images. One shortcoming of such transforms is their redundancy. This may set up a principal obstacle for reaching efficient coding schemes. Other
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Rania Boujelbene [email protected] L3S laboratory, University of Tunis-El Manar, Tunis, Tunisia
adaptive transforms such as ridgelets [14], wedgelets [15], directionlets [16] and bandelets [17], that allow to develop a sparse geometric representation of the images, have been presented and exploited in the context of image denoising [18] and image coding [19,20]. Recently, grouplets [21] and tetrolets [22] have bee
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