Browsing by Subject "Lifting structure"
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Item Open Access Directionally selective fractional wavelet transform using a 2-d non-separable unbalanced lifting structure(Springer, Berlin, Heidelberg, 2012) Keskin, Furkan; Çetin, A. EnisIn this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x 1[n] and x 2[n] whose average sampling periods are pT and qT, respectively. Fractions p and q are rational numbers satisfying the condition: 1/p+1/q=1. Filters used in the lifting structure are designed using the Lagrange interpolation formula. 2-d separable and non-separable extensions of the proposed fractional wavelet transform are developed. Using a non-separable unbalanced lifting structure, directional subimages for five different directions are obtained. © 2012 Springer-Verlag.Item Open Access Fractional wavelet transform using an unbalanced lifting structure(SPIE, 2011) Habiboǧlu, Y. Hakan; Köse, Kıvanç; Çetin, A. EnisIn this article, we introduce the concept of fractional wavelet transform. Using a two-channel unbalanced lifting structure it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT, respectively. Fractions p and q are rational numbers satisfying the condition: 1/p + 1/q = 1. The low-band sub-signal x 1[n] comes from [0, π/p] band and the high-band wavelet signal x 2[n] comes from (π/p, π] band of the original signal x[n]. Filters used in the liftingstructure are designed using the Lagrange interpolation formula. It is straightforward to extend the proposed fractional wavelet transform to two or higher dimensions in a separable or non separable manner. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).Item Open Access Linear and nonlinear temporal prediction employing lifting structures for scalable video coding(IEEE, 2006-09) Töreyin, B. Uğur; Trocan, M.; Pesquet-Popescu, B.; Çetin, A. EnisScalable 3D video codecs based on wavelet lifting structures have attracted recently a lot of attention, due to their compression performance comparable with that of state-of-art hybrid codecs. In this work, we propose a set of linear and nonlinear predictors for the temporal prediction step in lifting implementation. The predictor uses pixels on the motion trajectories of the frames in a window around the pixel to be predicted to improve the quality of prediction. Experimental results show that the video quality as well as PSNR values are improved with the proposed prediction method.Item Open Access Time-varying lifting structures for single-tree complexwavelet transform(IEEE, 2012) Keskin, Furkan; Çetin, A. EnisIn this paper, we describe a single-tree complex wavelet transform method using time-varying lifting structures. In the dualtree complex wavelet transform (DT-CWT), two different filterbanks are executed in parallel to analyze a given input signal, which increases the amount of data after analysis. DT-CWT leads to a redundancy factor of 2 d for d-dimensional signals. In the proposed single-tree complex wavelet transform (ST-CWT) structure, filters of the lifting filterbank switch back and forth between the two analysis filters of the DT-CWT. This approach does not increase the amount of output data as it is a critically sampled transform and it has the desirable properties of DT-CWT such as shift-invariance and directional selectivity. The proposed filterbank is capable of constructing a complex wavelet-like transform. Examples are presented. © 2012 IEEE.