Block-Based Adaptive Vector Lifting Schemes for Multichannel Image Coding

Adaptive lifting scheme with sparse criteria for image coding

“…Let us now adopt this probabilistic GGD model for the detail coefficients generated by a lifting structure. More precisely, at each resolution level j and orientation o (o {HL,LH,HH}), the wavelet coefficients x j+1 [11,43]:…”

“…columns), 2D NSLS provide smarter choices in the selection of the samples by using horizontal, vertical and oblique directions at the prediction step [9]. For example, quincunx lifting schemes were found to be suitable for coding satellite images acquired on a quincunx sampling grid [10,11]. In [12], a 2D wavelet decomposition comprising an adaptive update lifting step and three consecutive fixed prediction lifting steps was proposed.…”

“…To the best of our knowledge, most existing studies have mainly focused on the optimization of the prediction stage. In general, the goal of these studies is to introduce spatial adaptivity by varying the direction of the prediction step [15][16][17], the length of the prediction filters [18,19] and the coefficient values of the corresponding filters [9,11,15,20,21]. For instance, Gerek and Çetin [16] proposed a 2D edge-adaptive lifting scheme by considering three direction angles of prediction (0°, 45°, and 135°) and by selecting the orientation which leads to the smallest gradient.…”

“…In [9], the prediction filter coefficients are optimized with a least mean squares (LMS) type algorithm based on the prediction error. In addition to these adaptation techniques, the minimization of the detail signal entropy has also been investigated in [11,21]. In [11], the approach is limited to a quincunx structure and the optimization is performed in an empirical manner using the Nelder-Mead simplex algorithm due to the fact that the entropy is an implicit function of the prediction filter.…”

“…In addition to these adaptation techniques, the minimization of the detail signal entropy has also been investigated in [11,21]. In [11], the approach is limited to a quincunx structure and the optimization is performed in an empirical manner using the Nelder-Mead simplex algorithm due to the fact that the entropy is an implicit function of the prediction filter. However, such heuristic algorithms present the drawback that their convergence may be achieved at a local minimum of entropy.…”