Objective methods for assessing perceptual image quality have traditionally attempted to quantify the visibility of errors between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative framework for quality assessment based on the degradation of structural information. As a specific example of this concept, we develop a Structural Similarity Index and demonstrate its promise through a set of intuitive examples, as well as comparison to both subjective ratings and state-of-the-art objective methods on a database of images compressed with JPEG and JPEG2000.

Objective methods for assessing perceptual image quality traditionally attempt to quantify the visibility of errors (di#erences) between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative complementary framework for quality assessment based on the degradation of structural information. As a specific example of this concept, we develop a Structural Similarity Index and demonstrate its promise through a set of intuitive examples, as well as comparison to both subjective ratings and state-of-the-art objective methods on a database of images compressed with JPEG and JPEG2000. A MatLab implementation of the proposed algorithm is available online at http://www.cns.nyu.edu/~lcv/ssim/.

This paper presents a new wavelet-based image denoising method, which extends a recently emerged "geometrical" Bayesian framework. The new method combines these criteria for distinguishing supposedly useful coefficient from noise coefficient magnit:q54 tgni evolut47 across scales and spatA5 clust:q5A of large coefficients near image edges. These three crit546 are combined in a Bayesian framework. The spatD5 clust:q5] propert:5 are expressed in a prior model. Thest6[]A:q5D propertAA concerning coefficient magnit[:q andt:55 evolut4[ across scales are expressed in a joint condit:q]6 model. The three main noveltAA with respect to relat[ approaches are:(1)t he int760C7:q]0056: of wavelet coefficient are st0057:q]005 charact:q]55C and different local crit44C for dist]6:q]55C5 useful coefficient from noise are evaluat]6 (2) a joint condit:q]7 model is introduced, and (3) a novel anisot:q]7 Markov Random Field prior model is proposed. The results demonstrate an improved denoising performance over related earlier techniques.

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In this paper a novel stochastic image model in the transform domain is presented and its superior performance in image denoising applications is demonstrated. The proposed model exploits local subband image statistics and is based on geometrical priors. Contrarily to complex models based on local correlations, or to mixture models, the proposed model performs a partition of the image into non-overlapping regions with distinctive statistics. A close form analytical solution of the image denoising problem for AWGN is derived and its performance bounds are analyzed. Despite being very simple, the proposed stochastic image model provides a number of advantages in comparison to the existing approaches: (a) simplicity of stochastic image modeling; (b) completeness of the model, taking into account multiresolution, non-stationary image behavior, geometrical priors and providing an excellent fit to the global image statistics; (c) very low complexity of the algorithm; (d) tractability of the model and of the obtained results due to the closed-form solution and to the existence of analytical performance bounds; (e) extensibility to different transform domains, such as orthogonal, biorthogonal and overcomplete data representations. The results of benchmarking with the state-of-the-art image denoising methods demonstrate the superior performance of the proposed approach.

Abstract—Image denoising methods are often designed to minimize mean-squared error (MSE) within the subbands of a multiscale decomposition. However, most high-quality denoising results have been obtained with overcomplete representations, for which minimization of MSE in the subband domain does not guarantee optimal MSE performance in the image domain. We prove that, despite this suboptimality, the expected image-domain MSE resulting from applying estimators to subbands that are made redundant through spatial replication of basis functions (e.g., cycle spinning) is always less than or equal to that resulting from applying the same estimators to the original nonredundant representation. In addition, we show that it is possible to further exploit overcompleteness by jointly optimizing the subband estimators for image-domain MSE. We develop an extended version of Stein’s unbiased risk estimate (SURE) that allows us to perform this optimization adaptively, for each observed noisy image. We demonstrate this methodology using a new class of estimator formed from linear combinations of localized “bump ” functions that are applied either pointwise or on local neighborhoods of subband coefficients. We show through simulations that the performance of these estimators applied to overcomplete subbands and optimized for image-domain MSE is substantially better than that obtained when they are optimized within each subband. This performance is, in turn, substantially better than that obtained when they are optimized for use on a nonredundant representation. Index Terms—Bayesian estimation, cycle spinning, noise removal, overcomplete representation, , restoration, Stein’s unbiased risk estimator (SURE).

Abstract—Single sensor digital color still/video cameras capture images using a color filter array (CFA) and require color interpolation (demosaicking) to reconstruct full color images. The color reproduction has to combat sensor noises which are channel dependent. If untreated in demosaicking, sensor noises can cause color artifacts that are hard to remove later by a separate denoising process, because the demosaicking process complicates the noise characteristics by blending noises of different color channels. This paper presents a joint demosaicking-denoising approach to overcome this difficulty. The color image is restored from noisy mosaic data in two steps. First, the difference signals of color channels are estimated by linear minimum mean square-error estimation. This process exploits both spectral and spatial correlations to simultaneously suppress sensor noise and interpolation error. With the estimated difference signals, the full resolution green channel is recovered. The second step involves in a wavelet-based denoising process to remove the CFA channel-dependent noises from the reconstructed green channel. The red and blue channels are subsequently recovered. Simulated and real CFA mosaic data are used to evaluate the performance of the proposed joint demosaicking-denoising scheme and compare it with many recently developed sophisticated demosaicking and denoising schemes. Index Terms—Bayer pattern, color demosaicking, color filter array (CFA), denoising, wavelet. I.

... by 2-D wavelet packet transform. Experimentally it is demonstrated that this correlation varies from texture to texture. A new texture classification method, in which the simple linear regression model is employed into analyzing this correlation, is presented. Experiments show that this method significantly improves the texture classification rate in comparison with the multiresolution methods, including PSWT, TSWT, the Gabor transform, and some recently proposed methods derived from these.

Note: This is a revised version of the original SPIE 2006 paper in which a mistake was made in normalizing features before feeding them to the classifier: features from cover images and features from stego images were normalized differently. Due to this mistake, extra information about image classes was introduced to classification and the result was exceptionally good—the detection rate is close to 100%. We correct the mistake in this revision and most changes are made at the end of Sec. 4 and in Sec. 5 to present the correct results. Corresponding changes are also made in the conclusion (Sec. 6) while other sections remain intact. An accurate statistical model of cover images is essential to the success of both steganography and steganalysis. We study the statistics of the full-frame two-dimensional discrete Fourier transform (DFT) coefficients of natural images and show that the independently and identically distributed model with unit exponential distribution is not a sufficiently accurate description of the statistics of normalized image periodograms. Consequently, the stochastic quantization index modulation (QIM) algorithm that aims at preserving this model is detectable in principle. To discriminate the resulted stegoimages from cover images, we train a learning system on them. Building upon a state-of-the-art steganalysis method using the statistical moments of wavelet characteristic functions, we propose new features that are more sensitive to data embedding. The addition of these features significantly improves the steganalyzer’s receiver operating characteristic (ROC) curve.

We explore the use of neural networks to predict wavelet coefficients for image compression. We show that by reducing the variance of the residual coefficients, the nonlinear prediction can be used to reduce the length of the compressed bitstream. We report results on several network architectures and training methodologies; some pitfalls of the approach are examined and explained.