A nonlinear Stein based estimator for multichannel image denoising

The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A multivariate statistical approach is adopted to take into account both the spatial and the inter-component correlations existing between the different wavelet subbands. More precisely, we propose a new parametric nonlinear estimator which generalizes many reported denoising methods. The derivation of the optimal parameters is achieved by applying Stein's principle in the multivariate case. Experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising technique

Wavelet Based Color Image Denoising through a Bivariate Pearson Distribution

In this paper we proposed an efficient algorithm for Colo r Image Denoising through a Bivariate Pearson Distribution using Wavelet Which is based on Bayesian denoising and if Bayesian denoising is used for recovering image from the noisy image the performance is strictly depend on the correctness of the distribution that is used to describe the data. In the denoising process we require a selection of p roper model for distribution. To describe the image data bivariate pearson distribution is used and Gaussian distribution is used to describe the noise particles in this paper. For gray scale image lots of extensive works has been don e in this field but fo r colour image denoising using bivariate pearson distribution based on bayesian denoising gives us tremendous result for analy sing coloured images which can be used in several advanced applications. The bivariate probability density function (pdf) takes in t o account the Gaussian dependency among wavelet coefficients. The experimental results show that the proposed technique outperforms sev eral exiting methods both visually and in terms of peak signal - to - noise ratio (PSNR)

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

Optical Coherence Tomography Noise Reduction Using Anisotropic Local Bivariate Gaussian Mixture Prior in 3D Complex Wavelet Domain

In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR

Multi-Modal Enhancement Techniques for Visibility Improvement of Digital Images

Image enhancement techniques for visibility improvement of 8-bit color digital images based on spatial domain, wavelet transform domain, and multiple image fusion approaches are investigated in this dissertation research. In the category of spatial domain approach, two enhancement algorithms are developed to deal with problems associated with images captured from scenes with high dynamic ranges. The first technique is based on an illuminance-reflectance (I-R) model of the scene irradiance. The dynamic range compression of the input image is achieved by a nonlinear transformation of the estimated illuminance based on a windowed inverse sigmoid transfer function. A single-scale neighborhood dependent contrast enhancement process is proposed to enhance the high frequency components of the illuminance, which compensates for the contrast degradation of the mid-tone frequency components caused by dynamic range compression. The intensity image obtained by integrating the enhanced illuminance and the extracted reflectance is then converted to a RGB color image through linear color restoration utilizing the color components of the original image. The second technique, named AINDANE, is a two step approach comprised of adaptive luminance enhancement and adaptive contrast enhancement. An image dependent nonlinear transfer function is designed for dynamic range compression and a multiscale image dependent neighborhood approach is developed for contrast enhancement. Real time processing of video streams is realized with the I-R model based technique due to its high speed processing capability while AINDANE produces higher quality enhanced images due to its multi-scale contrast enhancement property. Both the algorithms exhibit balanced luminance, contrast enhancement, higher robustness, and better color consistency when compared with conventional techniques. In the transform domain approach, wavelet transform based image denoising and contrast enhancement algorithms are developed. The denoising is treated as a maximum a posteriori (MAP) estimator problem; a Bivariate probability density function model is introduced to explore the interlevel dependency among the wavelet coefficients. In addition, an approximate solution to the MAP estimation problem is proposed to avoid the use of complex iterative computations to find a numerical solution. This relatively low complexity image denoising algorithm implemented with dual-tree complex wavelet transform (DT-CWT) produces high quality denoised images

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

A CURE for noisy magnetic resonance images: Chi-square unbiased risk estimation

In this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi-square random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon state-of-the-art methods for both simulated and actual magnetic resonance image data.Comment: 30 double-spaced pages, 11 figures; submitted for publicatio