Expected Patch Log Likelihood Research Articles

Dictionary learning-based denoising algorithm with expected patch log likelihood in diffusion-weighted magnetic resonance image

Dictionary learning-based denoising algorithm with expected patch log likelihood in diffusion-weighted magnetic resonance image

Super-resolution of Retinal Optical Coherence Tomography Images Using Statistical Modeling.

Optical coherence tomography (OCT) imaging has emerged as a promising diagnostic tool, especially in ophthalmology. However, speckle noise and downsampling significantly degrade the quality of OCT images and hinder the development of OCT-assisted diagnostics. In this article, we address the super-resolution (SR) problem of retinal OCT images using a statistical modeling point of view. In the first step, we utilized Weibull mixture model (WMM) as a comprehensive model to establish the specific features of the intensity distribution of retinal OCT data, such as asymmetry and heavy tailed. To fit the WMM to the low-resolution OCT images, expectation-maximization algorithm is used to estimate the parameters of the model. Then, to reduce the existing noise in the data, a combination of Gaussian transform and spatially constraint Gaussian mixture model is applied. Now, to super-resolve OCT images, the expected patch log-likelihood is used which is a patch-based algorithm with multivariate GMM prior assumption. It restores the high-resolution (HR) images with maximum a posteriori (MAP) estimator. The proposed method is compared with some well-known super-resolution algorithms visually and numerically. In terms of the mean-to-standard deviation ratio (MSR) and the equivalent number of looks, our method makes a great superiority compared to the other competitors. The proposed method is simple and does not require any special preprocessing or measurements. The results illustrate that our method not only significantly suppresses the noise but also successfully reconstructs the image, leading to improved visual quality.

EPLL image denoising with multi-feature dictionaries

The expected patch log likelihood (EPLL) is a patch-prior based denoising model that has become a popular tool in image restoration for its outstanding edge preservation and noise reduction abilities. However, without considering the geometrical feature of patches, the EPLL removes numerous important details and frequently suffers from the staircase effect, residual noise and artifacts. To preserve more detailed information and suppress the generation of artifacts, we propose a novel EPLL denoising model with multi-feature dictionaries (MFDs) and adaptive regularization parameters in this paper. In the proposed method, to exploit the statistical and geometrical characteristics of patches, two feature layers are designed before training the Gaussian mixture model (GMM). In the first layer, the within-class variance minimum (WCVM) method is used to learn the statistical features of patches. In the second layer, two geometrical characteristic dictionaries (GCDs) are trained. In the denoising phase, we select the corresponding dictionary for each patch. Then, each patch is denoised independently. Moreover, the mean localized spectral response (MLSR) based regularization parameters are employed in the proposed method, which is spatial self-adaptive and robust to noise. Extensive experiments demonstrate that our approach achieves desired performance in both detail preservation and artifact suppression compared to many existing denoising methods.

EPLL image restoration with a bounded asymmetrical Student’s-t mixture model

The expected patch log-likelihood (EPLL) model is a patch prior-based image restoration method which received extensive attention in image processing in recent years for its outstanding ability to preserve the detail and structure. However, due to using the Gaussian mixture model (GMM) with the noise sensitivity as the local prior, the EPLL model suffers from undesired artifact and poor robustness frequently. In this paper, to restrain the generation of artifact of EPLL model, we replace the GMM with a bounded asymmetrical Student’s-t mixture model (BASMM), which is sufficiently flexible to fit different shapes of image data, such as non-Gaussian, non-symmetric, and bounded support data. Then, the anisotropic nonlocal self-similarity (ANSS) based regularization parameters are designed to improve the robustness of the proposed model. Experimental results demonstrate the competitiveness of our proposed model compared with that of state-of-the-art methods in performance both visually and quantitatively.

Low-frequency seismic random noise attenuation based on EPLL-TV under double prior constraints

The expected patch log likelihood (EPLL) method utilizes the learned Gaussian mixture model (GMM) as a prior for white Gaussian noise removal, so that every patch from noisy data is likely under the prior and the global morphology is remained along with denoising. For suppressing the low-frequency seismic random noise having similar waveforms to the signals, we propose an Expected Patch Log Likelihood-Total Variation (EPLL-TV) algorithm, which is constrained by the EPLL prior and the total variation (TV) prior. In the denoising process, the TV prior introduces the structural features of the current data and restrains the random noise by enhancing the gradient sparsity of seismic data. Hence, the EPLL-TV algorithm is able to choose the Gaussian component which is closest to the features of signals from pre-learned general prior of EPLL, although the features in the patch are severely disturbed by the low-frequency noise. Then the seismic events with complex structures can be accurately restored by the chosen Gaussian component, which provides more reliable structures for denoising via the TV prior. We use the alternating direction method of multipliers (ADMM) to solve the proposed optimization model with double constraints and reconstruct the data in Fourier domain to reduce computational complexity. The results of the synthetic and field seismic data demonstrate that the proposed EPLL-TV method is superior to the other methods mentioned in our paper in terms of recovering the seismic events with complex structures and suppressing the low-frequency seismic random noise which has similar waveforms to the signals.

Image patch prior learning based on random neighbourhood resampling for image denoising

Image patch priors become a popular tool for image denoising. The Gaussian mixture model (GMM) is remarkably effective in modelling natural image patches. However, GMM prior learning using the expectation maximisation (EM) algorithm is sensitive to the initialisation, often leading to low convergence rate of parameter estimation. In this study, a novel sampling method called random neighbourhood resampling (RNR) is proposed to improve the accuracy and efficiency of parameter estimation. An enhanced GMM (EGMM) learning algorithm is further developed by incorporating RNR into the EM algorithm to initialise and update the GMM prior. The learned EGMM prior is applied in the expected patch log-likelihood (EPLL) framework for image denoising. The effectiveness and performance of the proposed RNR and EGMM algorithm are demonstrated via extensive experimental results comparing with the state-of-the-art image denoising methods, the experimental results show the higher PSNR result of the denoised images using the proposed method. Meanwhile, the authors verified that the proposed method can efficiently reduce the time of image denoising compared with the basic EPLL method.

Patch classification based EPLL with mixed GMM for nonstationary seismic random noise attenuation

We propose an expected patch log likelihood (EPLL) based denoising method for nonstationary seismic random noise which has spatiotemporally varying variance, by incorporating the patch classification and mixed Gaussian mixture model (GMM), named PC-EPLL. In this method, the overlapping patches extracted from the noisy data are clustered into several classes based on a binary-tree, so that random noise in each class remains stationary. Thus the EPLL can denoise each class respectively by assigning proper parameters related to the noise characteristics of the class. Moreover, we combine the generic GMM learned from the nature image database and the target GMM learned from the seismic data by utilizing the weights related to the structural features of seismic data. In this way, the mixed GMM effectively captures the complex seismic features in a flexible learning way, and alleviates the over-fitting of the target GMM that is induced by the limited seismic training samples. Therefore, the PC-EPLL is capable of reconstructing the seismic signals from nonstationary seismic random noise. Synthetic and field seismic data are used to evaluate denoising performance of the proposed method. The results show that the proposed method achieves better performances in seismic event preservation and nonstationary random noise attenuation than the EPLL with the generic GMM and is superior to several state-of-the-art seismic denoising methods.

A Novel Bayesian Patch-Based Approach for Image Denoising

Recently patch-based image denoising techniques have gained the attention of researchers as it is being used in numerous image denoising applications. This article is proposing a new Bayesian Patch-based image denoising algorithm using Quaternion Wavelet Transform (QWT) for grayscale images. In the proposed work, a patch model has been used instead of the Gibbs distribution based energy model. Experimental results indicate that the proposed algorithm effectively diminishes noise. The results of the developed approach are also compared with other efficient image denoising algorithms such as Expected Patch Log Likelihood (EPLL), Block-matching and 3D filtering (BM3D), Patch-Based Locally Optimal Wiener (PLOW), Weighted Nuclear Norm Minimization (WNNM), Hybrid Robust Bilateral Filter-Total Variation Filter (RBF-TVF) and Hybrid Total Variation Filter-Weighted Bilateral Filter (TVF-WBF) methods. The comparison revealed that the outcomes of the given approach are much sharper, clearer, and having the highest quality in comparison with other patch-based methods.

New Adaptive Regularization Parameter Selection Based on Expected Patch Log Likelihood

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An Expected Patch Log Likelihood Denoising Method Based on Internal and External Image Similarity

An Expected Patch Log Likelihood Denoising Method Based on Internal and External Image Similarity

A Unified View on Patch Aggregation

Patch-based methods are widely used in various topics of image processing, such as image restoration or image editing and synthesis. Patches capture local image geometry and structure and are much easier to model than whole images: in practice, patches are small enough to be represented by simple multivariate priors. An important question arising in all patch-based methods is the one of patch aggregation. For instance, in image restoration, restored patches are usually not compatible, in the sense that two overlapping restored patches do not necessarily yield the same values to their common pixels. A standard way to overcome this difficulty is to see the values provided by different patches at a given pixel as independent estimators of a true unknown value and to aggregate these estimators. This aggregation step usually boils down to a simple average, with uniform weights or with weights depending on the trust we have on these different estimators. In this paper, we propose a probabilistic framework aiming at a better understanding of this crucial and often neglected step. The key idea is to see the aggregation of two patches as a fusion between their models rather than a fusion of estimators. The proposed fusion operation is pretty intuitive and generalizes previous aggregation methods. It also yields a novel interpretation of the Expected Patch Log Likelihood (EPLL) proposed in Zoran and Weiss (in: 2011 IEEE international conference on computer vision (ICCV), 2011).

Multi-channel expected patch log likelihood for color image denoising

Due to its flexibility and good restoration performance, the Expected Patch Log Likelihood (EPLL) method has attracted extensive attention and has been further developed. However, the basic EPLL method is mainly applied for gray image restoration. For color image denoising with different channel noise levels, concatenating the RGB values into a vector and applying the basic EPLL directly can produce false colors and artifacts. In this paper, a Multi-Channel Expected Patch Log Likelihood (MC-EPLL) method is proposed for color image denoising with different channel noise levels. Considering the within and between channel correlation, the noise model of the concatenated vector of RGB channels can be constructed as a Matrix Normal Distribution. Under the KL divergence framework, the MC-EPLL model can be derived by combining the noise model and Gaussian Mixture Model (GMM) based patch prior. Based on the half quadratic splitting (HQS) strategy, the MC-EPLL model is decomposed into two sub-minimization problems and the closed-form solution of each sub-problem can be obtained. Experiments show the feasibility and superiority of the proposed MC-EPLL over the compared denoising methods.

Selection of regularization parameter in GMM based image denoising method

Currently, the image denoising methods using Gaussian mixture model to learn image prior have received much attention. Among these methods, expected patch log likelihood based image denoising appro...

Selection of regularization parameter in GMM based image denoising method

Currently, the image denoising methods using Gaussian mixture model to learn image prior have received much attention. Among these methods, expected patch log likelihood based image denoising approach has been shown to be surprisingly competitive in image restoration. However, recent related works generally utilize global regularization parameter that influences the performance of denoising algorithm. In this paper, with the consideration that the Gaussian mixture model has the capability of clustering, we propose an adaptive estimation method of regularization parameter for expected patch log likelihood based image denoising. Our method jointly employs the Lagrange multiplier technique and entropy concept to select regularization parameter for each underlying cluster. Experimental results illustrate the relatively good performance of our image denoising method in terms of visual improvement and peak signal to noise ratio.

Blind deblurring with sparse representation via external patch priors

In this paper, a blind image deblurring method is proposed using sparse representation with external patch priors. Different from traditional sparse-based methods that employ only internal priors from blurred images, additional external information is adopted to reconstruct latent images. In details, the Expected Patch Log Likelihood (EPLL) is introduced as a useful tool to describe external patch priors with a pre-trained Gaussian mixture model. With a set of operations, the EPLL is subsequently incorporated as a regularization term into the existing sparse-based deblurring model. Meanwhile, the dictionary is also carefully designed for each patch of the latent image, where atoms are obtained from the covariance matrix of the corresponding Gaussian component. A deblurring framework is further presented along with our sparse-based model. The solutions are respectively given to efficiently optimize the latent image and the blur kernel with an iterative procedure. The experiments demonstrate that our proposed algorithm achieves a competitive performance compared with the state-of-the-arts. Especially, it not only can obtain more accurate kernels for the deblurring, but also outperforms in noise reduction and artifact suppression for the restored images.

Image Denoising with Generalized Gaussian Mixture Model Patch Priors

Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular expected patch log-likelihood (EPLL) algorithm. E...

Accelerating GMM-Based Patch Priors for Image Restoration: Three Ingredients for a Speed-Up.

Image restoration methods aim to recover the underlying clean image from corrupted observations. The expected patch log-likelihood (EPLL) algorithm is a powerful image restoration method that uses a Gaussian mixture model (GMM) prior on the patches of natural images. Although it is very effective for restoring images, its high runtime complexity makes the EPLL ill-suited for most practical applications. In this paper, we propose three approximations to the original EPLL algorithm. The resulting algorithm, which we call the fast-EPLL (FEPLL), attains a dramatic speed-up of two orders of magnitude over EPLL while incurring a negligible drop in the restored image quality (less than 0.5 dB). We demonstrate the efficacy and versatility of our algorithm on a number of inverse problems, such as denoising, deblurring, super-resolution, inpainting, and devignetting. To the best of our knowledge, the FEPLL is the first algorithm that can competitively restore a pixel image in under 0.5 s for all the degradations mentioned earlier without specialized code optimizations, such as CPU parallelization or GPU implementation.

Image denoising via patch-based adaptive Gaussian mixture prior method

Although the expected patch log likelihood (EPLL) achieves good performance for denoising, an inherent nonadaptive problem exists. To solve this problem, an adaptive learning is introduced into the EPLL in this paper. Inspired from the structured sparse dictionary, an adaptive Gaussian mixture model (GMM) is proposed based on patch priors. The maximum a posteriori estimation is employed to cluster and update the image patches. Also, the new image patches are used to update the GMM. We perform these two steps alternately until the desired denoised results are achieved. Experimental results show that the proposed denoising method outperforms the existing image denoising algorithms.

Multi-Scale Patch-Based Image Restoration.

Many image restoration algorithms in recent years are based on patch processing. The core idea is to decompose the target image into fully overlapping patches, restore each of them separately, and then merge the results by a plain averaging. This concept has been demonstrated to be highly effective, leading often times to the state-of-the-art results in denoising, inpainting, deblurring, segmentation, and other applications. While the above is indeed effective, this approach has one major flaw: the prior is imposed on intermediate (patch) results, rather than on the final outcome, and this is typically manifested by visual artifacts. The expected patch log likelihood (EPLL) method by Zoran and Weiss was conceived for addressing this very problem. Their algorithm imposes the prior on the patches of the final image, which in turn leads to an iterative restoration of diminishing effect. In this paper, we propose to further extend and improve the EPLL by considering a multi-scale prior. Our algorithm imposes the very same prior on different scale patches extracted from the target image. While all the treated patches are of the same size, their footprint in the destination image varies due to subsampling. Our scheme comes to alleviate another shortcoming existing in patch-based restoration algorithms--the fact that a local (patch-based) prior is serving as a model for a global stochastic phenomenon. We motivate the use of the multi-scale EPLL by restricting ourselves to the simple Gaussian case, comparing the aforementioned algorithms and showing a clear advantage to the proposed method. We then demonstrate our algorithm in the context of image denoising, deblurring, and super-resolution, showing an improvement in performance both visually and quantitatively.

Learning to Diversify Patch-Based Priors for Remote Sensing Image Restoration

The restoration of clean remote sensing images from the degraded images is usually an ill-posed problem. A feasible solution for the problem is incorporating various priors into restoration procedure as constrained conditions. Recently, the patch-based Gaussian mixture model (GMM) priors became popular. However, the learning of patch-based GMM priors usually assumes the components of the GMM are independent and identically distributed (i.i.d.). The assumption means that two components could model the same training samples, and thus a possible decrease in model’s description ability. This work presents a new learning method to diversify the patch-based GMM priors through modeling the GMM’s parameters as a determinantal point process (DPP). The introduction of DPP allows us to specify a preference for diversity in patch-based GMM using a positive definite kernel function and thus to increase the model’s description ability for a given model complexity. Furthermore, under the expected patch log-likelihood (EPLL) restoration framework, we further introduce the diversified patch-based GMM priors into remote sensing literature and develop new remote sensing image restoration algorithms. The extensive experiments for denoising and deblurring of remote sensing images demonstrated that the proposed algorithms produced better restoration results than other methods that already proven to perform well in the literature.