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.
Recovering images from corrupted observations is necessary for many real-world applications. In this paper, we propose a unified framework to perform progressive image recovery based on hybrid graph Laplacian regularized regression. We first construct a multiscale representation of the target image by Laplacian pyramid, then progressively recover the degraded image in the scale space from coarse to fine so that the sharp edges and texture can be eventually recovered. On one hand, within each scale, a graph Laplacian regularization model represented by implicit kernel is learned, which simultaneously minimizes the least square error on the measured samples and preserves the geometrical structure of the image data space. In this procedure, the intrinsic manifold structure is explicitly considered using both measured and unmeasured samples, and the nonlocal self-similarity property is utilized as a fruitful resource for abstracting a priori knowledge of the images. On the other hand, between two successive scales, the proposed model is extended to a projected high-dimensional feature space through explicit kernel mapping to describe the interscale correlation, in which the local structure regularity is learned and propagated from coarser to finer scales. In this way, the proposed algorithm gradually recovers more and more image details and edges, which could not been recovered in previous scale. We test our algorithm on one typical image recovery task: impulse noise removal. Experimental results on benchmark test images demonstrate that the proposed method achieves better performance than state-of-the-art algorithms.
In this paper, we propose a new psychovisual quality metric of images based on recent developments in brain theory and neuroscience, particularly the free-energy principle. The perception and understanding of an image is modeled as an active inference process, in which the brain tries to explain the scene using an internal generative model. The psychovisual quality is thus closely related to how accurately visual sensory data can be explained by the generative model, and the upper bound of the discrepancy between the image signal and its best internal description is given by the free energy of the cognition process. Therefore, the perceptual quality of an image can be quantified using the free energy. Constructively, we develop a reduced-reference free-energy-based distortion metric (FEDM) and a no-reference free-energy-based quality metric (NFEQM). The FEDM and the NFEQM are nearly invariant to many global systematic deviations in geometry and illumination that hardly affect visual quality, for which existing image quality metrics wrongly predict severe quality degradation. Although with very limited or even without information on the reference image, the FEDM and the NFEQM are highly competitive compared with the full-reference SSIM image quality metric on images in the popular LIVE database. Moreover, FEDM and NFEQM can measure correctly the visual quality of some model-based image processing algorithms, for which the competing metrics often contradict with viewers opinions.
We investigate the problem of designing adaptive sequential linear predictors for the class of piecewise autoregressive multidimensional signals, and adopt an approach of minimum description length (MDL) to determine the order of the predictor and the support on which the predictor operates. The design objective is to strike a balance between the bias and variance of the prediction errors in the MDL criterion. The predictor design problem is particularly interesting and challenging for multidimensional signals (e.g., images and videos) because of the increased degree of freedom in choosing the predictor support. Our main result is a new technique of sequentializing a multidimensional signal into a sequence of nested contexts of increasing order to facilitate the MDL search for the order and the support shape of the predictor, and the sequentialization is made adaptive on a sample by sample basis. The proposed MDL-based adaptive predictor is applied to lossless image coding, and its performance is empirically established to be the best among all the results that have been published till present.
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