Lossless Predictive Coding for Images With Bayesian Treatment

Abstract

Adaptive predictor has long been used for lossless predictive coding of images. Most of existing lossless predictive coding techniques mainly focus on suitability of prediction model for training set with the underlying assumption of local consistency, which may not hold well on object boundaries and cause large predictive error. In this paper, we propose a novel approach based on the assumption that local consistency and patch redundancy exist simultaneously in natural images. We derive a family of linear models and design a new algorithm to automatically select one suitable model for prediction. From the Bayesian perspective, the model with maximum posterior probability is considered as the best. Two types of model evidence are included in our algorithm. One is traditional training evidence, which represents the models’ suitability for current pixel under the assumption of local consistency. The other is target evidence, which is proposed to express the preference for different models from the perspective of patch redundancy. It is shown that the fusion of training evidence and target evidence jointly exploits the benefits of local consistency and patch redundancy. As a result, our proposed predictor is more suitable for natural images with textures and object boundaries. Comprehensive experiments demonstrate that the proposed predictor achieves higher efficiency compared with the state-of-the-art lossless predictors.

A Stochastic Model for Block Segmentation of Images Based on the Quadtree and the Bayes Code for It

“…This can be regarded as b being a parameter of the two-sided geometric distribution andb(x t−1 ) being its tuning method. In other studies [12][13][14][15][16][17], the authors proposed coding procedures f (x t−1 ; a, b, c a ) in which coefficients c a of each linear predictor are tuned by a certain methodc a (x t−1 ), e.g., the least squares method or weighted least squares method. In [18,19], the authors proposed coding procedures f (x t−1 ; a, b, c a , w) in which multiple predictors are combined according to another tuning parameter w that represents the weights of each predictor.…”

“…However, there are some coding procedures f (x; a) [11][12][13][14][16][17][18][19][20]23] whose tuning parameter a can be regarded as a statistical parameter of an implicitly assumed statistical generative model p(x|a) by changing the viewpoint. (In some of these studies, the assumption of the stochastic generative model is claimed, but the distinction between the stochastic generative model and the code length assign vector is ambiguous, and the discussion about the difference between the expected code length and the entropy of the stochastic generative model is insufficient.)…”

A Stochastic Model of Block Segmentation Based on the Quadtree and the Bayes Code for It

“…However, there are some coding procedures f (x; a) [10]- [13], [15]- [19], [22] whose tuning parameter a can be regarded as a statistical parameter of an implicitly assumed statistical generative model p(x|a) by changing the viewpoint 3 . Further, its parameter tuning methodã(x) could be regraded as an heuristic approximation of the information-theoretically optimal estimationâ(x) ≈ã(x).…”

“…The previous studies based on this approach are [23] and [24]. In [23], they proposed a two-dimensional autoregressive model and the optimal coding algorithm by interpreting the basic procedure [10]- [12], [15], [22] of the predictive coding as a stochastic generative model. In [24], they proposed a two-dimensional autoregressive hidden Markov model by interpreting the predictor weighting procedure around a diagonal edge [17] as a stochastic generative model.…”

Fast Context-Adaptive Bit-Depth Enhancement via Linear Interpolation

“…A commonly used prior is the notion of smoothness with the assumption that image signals tend to be piece-wise smooth. It has achieved great success for numerous inverse problems in image processing field such as compression [5], [6], image quality assessment [7], [8], and restoration [9], [10]. And as a typical inverse problem, BDE has no reason to be an exception.…”