Geometric nonlinear diffusion filter and its application to X-ray imaging

<p>Abstract</p> <p>Background</p> <p>Denoising with edge preservation is very important in digital x-ray imaging since it may allow us to reduce x-ray dose in human subjects without noticeable degradation of the image quality. In denoising filter design for x-ray imaging, edge preservation as well as noise reduction is of great concern not to lose detailed spatial information for accurate diagnosis. In addition to this, fast computation is also important since digital x-ray images are mostly comprised of large sized matrices.</p> <p>Methods</p> <p>We have developed a new denoising filter based on the nonlinear diffusion filter model. Rather than employing four directional gradients around the pixel of interest, we use geometric parameters derived from the local pixel intensity distribution in calculating the diffusion coefficients in the horizontal and vertical directions. We have tested the filter performance, including edge preservation and noise reduction, using low dose digital radiography and micro-CT images.</p> <p>Results</p> <p>The proposed denoising filter shows performance similar to those of nonlinear anisotropic diffusion filters (ADFs), one Perona-Malik ADF and the other Weickert's ADF in terms of edge preservation and noise reduction. However, the computation time has been greatly reduced.</p> <p>Conclusions</p> <p>We expect the proposed denoising filter can be greatly used for fast noise reduction particularly in low-dose x-ray imaging.</p

Digital Radiographic Image Denoising Via Wavelet-Based Hidden Markov Model Estimation

This paper presents a technique for denoising digital radiographic images based upon the wavelet-domain Hidden Markov tree (HMT) model. The method uses the Anscombe’s transformation to adjust the original image, corrupted by Poisson noise, to a Gaussian noise model. The image is then decomposed in different subbands of frequency and orientation responses using the dual-tree complex wavelet transform, and the HMT is used to model the marginal distribution of the wavelet coefficients. Two different correction functions were used to shrink the wavelet coefficients. Finally, the modified wavelet coefficients are transformed back into the original domain to get the denoised image. Fifteen radiographic images of extremities along with images of a hand, a line-pair, and contrast–detail phantoms were analyzed. Quantitative and qualitative assessment showed that the proposed algorithm outperforms the traditional Gaussian filter in terms of noise reduction, quality of details, and bone sharpness. In some images, the proposed algorithm introduced some undesirable artifacts near the edges

Edge Preservation in Nonlinear Diffusion Filtering

Edge Preservation in Nonlinear Diffusion Filtering Mohammad Reza Hajiaboli, Ph.D. Concordia University, 2012 Image denoising techniques, in which the process of noise diffusion is modeled as a nonlinear partial differential equation, are well known for providing low-complexity solutions to the denoising problem with a minimal amount of image artifacts. In discrete settings of these nonlinear models, the objective of providing a good noise removal while preserving the image edges is heavily dependent on the kernels, diffusion functions and the associated contrast parameters employed by these nonlinear diffusion techniques. This thesis makes an in-depth study of the roles of the kernels and contrast parameters with a view to providing an effective solution to the problem of denoising of the images contaminated with stationary and signal-dependent noise. Within the above unified theme, this thesis has two major parts. In the first part of this study, the impact of anisotropic behavior of the Laplacian operator on the capabilities of nonlinear diffusion filters in preserving the image edges in different orientations is investigated. Based on this study, an analytical scheme is devised to obtain a spatially-varying kernel that adapt itself to the diffusivity function. The proposed edge-adaptive Laplacian kernel is then incorporated into various nonlinear diffusion filters for denoising of images contaminated by additive white Gaussian noise. The performance optimality of the the existing nonlinear diffusion techniques is generally based on the assumption that the noise and signal are uncorrelated. However, in many applications, such as in medical imaging systems and in remote sensing where the images are degraded by Poisson noise, this assumption is not valid. As such, in the second part of the thesis, a study is undertaken for denoising of images contaminated by Poisson noise within the framework of the Perona-Malik nonlinear diffusion filter. Specifically, starting from a Skellam distribution model of the gradient of the Poisson-noise corrupted images and following the diffusion mechanism of the nonlinear filter, a spatially and temporally varying contrast parameter is designed. It is shown that the nonlinear diffusion filters employing the new Laplacian kernel supports the extremum principle and that the proposed contrast parameter satisfies the sufficient conditions for observance of the scale-space properties. Extensive experiments are performed throughout the thesis to demonstrate the effectiveness and validity of the various schemes and techniques developed in this investigation. The simulation results of applying the new Laplacian kernel to a number of nonlinear diffusion filters show its distinctive advantages over the conventional Rosenfeld and Kak kernel, in terms of the filters' noise reduction and edge preservation capabilities for images corrupted by additive white Gaussian noise. The simulation results of incorporating the proposed spatially- and temporally-varying contrast parameter into the Perona-Malik nonlinear diffusion filter demonstrate a performance much superior to that provided by some of the other state-of-the-art techniques in denoising images corrupted by Poisson noise

Wavelet-based noise reduction of cDNA microarray images

The advent of microarray imaging technology has lead to enormous progress in the life sciences by allowing scientists to analyze the expression of thousands of genes at a time. For complementary DNA (cDNA) microarray experiments, the raw data are a pair of red and green channel images corresponding to the treatment and control samples. These images are contaminated by a high level of noise due to the numerous noise sources affecting the image formation. A major challenge of microarray image analysis is the extraction of accurate gene expression measurements from the noisy microarray images. A crucial step in this process is denoising, which consists of reducing the noise in the observed microarray images while preserving the signal information as much as possible. This thesis deals with the problem of developing novel methods for reducing noise in cDNA microarray images for accurate estimation of the gene expression levels. Denoising methods based on the wavelet transform have shown significant success when applied to natural images. However, these methods are not very efficient for reducing noise in cDNA microarray images. An important reason for this is that existing methods are only capable of processing the red and green channel images separately. In doing so. they ignore the signal correlation as well as the noise correlation that exists between the wavelet coefficients of the two channels. The primary objective of this research is to design efficient wavelet-based noise reduction algorithms for cDNA microarray images that take into account these inter-channel dependencies by 'jointly' estimating the noise-free coefficients in both the channels. Denoising algorithms are developed using two types of wavelet transforms, namely, the frequently-used discrete wavelet transform (DWT) and the complex wavelet transform (CWT). The main advantage of using the DWT for denoising is that this transform is computationally very efficient. In order to obtain a better denoising performance for microarray images, however, the CWT is preferred to DWT because the former has good directional selectivity properties that are necessary for better representation of the circular edges of spots. The linear minimum mean squared error and maximum a posteriori estimation techniques are used to develop bivariate estimators for the noise-free coefficients of the two images. These estimators are derived by utilizing appropriate joint probability density functions for the image coefficients as well as the noise coefficients of the two channels. Extensive experimentations are carried out on a large set of cDNA microarray images to evaluate the performance of the proposed denoising methods as compared to the existing ones. Comparisons are made using standard metrics such as the peak signal-to-noise ratio (PSNR) for measuring the amount of noise removed from the pixels of the images, and the mean absolute error for measuring the accuracy of the estimated log-intensity ratios obtained from the denoised version of the images. Results indicate that the proposed denoising methods that are developed specifically for the microarray images do, indeed, lead to more accurate estimation of gene expression levels. Thus, it is expected that the proposed methods will play a significant role in improving the reliability of the results obtained from practical microarray experiments

Probabilistic modeling of wavelet coefficients for processing of image and video signals

Statistical estimation and detection techniques are widely used in signal processing including wavelet-based image and video processing. The probability density function (PDF) of the wavelet coefficients of image and video signals plays a key role in the development of techniques for such a processing. Due to the fixed number of parameters, the conventional PDFs for the estimators and detectors usually ignore higher-order moments. Consequently, estimators and detectors designed using such PDFs do not provide a satisfactory performance. This thesis is concerned with first developing a probabilistic model that is capable of incorporating an appropriate number of parameters that depend on higher-order moments of the wavelet coefficients. This model is then used as the prior to propose certain estimation and detection techniques for denoising and watermarking of image and video signals. Towards developing the probabilistic model, the Gauss-Hermite series expansion is chosen, since the wavelet coefficients have non-compact support and their empirical density function shows a resemblance to the standard Gaussian function. A modification is introduced in the series expansion so that only a finite number of terms can be used for modeling the wavelet coefficients with rendering the resulting PDF to become negative. The parameters of the resulting PDF, called the modified Gauss-Hermite (NIGH) PDF, are evaluated in terms of the higher-order sample-moments. It is shown that the MGH PDF fits the empirical density function better than the existing PDFs that use a limited number of parameters do. The proposed MGH PDF is used as the prior of image and video signals in designing maximum a posteriori and minimum mean squared error-based estimators for denoising of image and video signals and log-likelihood ratio-based detector for watermarking of image signals. The performance of the estimation and detection techniques are then evaluated in terms of the commonly used metrics. It is shown through extensive experimentations that the estimation and detection techniques developed utilizing the proposed MGH PDF perform substantially better than those that utilize the conventional PDFs. These results confirm that the superior fit of the MGH PDF to the empirical density function resulting from the flexibility of the MGH PDF in choosing the number of parameters, which are functions of higher-order moments of data, leads to the better performance. Thus, the proposed MGH PDF should play a significant role in wavelet-based image and video signal processin