Wavelet-based Image Denoising Research Articles

Statistical Wavelet-based Image Denoising using Scale Mixture of Normal Distributions with Adaptive Parameter Estimation

Removing noise from images is a challenging problem in digital image processing. This paper presents an image denoising method based on a maximum a posteriori (MAP) density function estimator, which is implemented in the wavelet domain because of its energy compaction property. The performance of the MAP estimator depends on the proposed model for noise-free wavelet coefficients. Thus in the wavelet based image denoising, selecting a proper model for wavelet coefficients is very important. In this paper, we model wavelet coefficients in each sub-band by heavy-tail distributions that are from scale mixture of normal distribution family. The parameters of distributions are estimated adaptively to model the correlation between the coefficient amplitudes, so the intra-scale dependency of wavelet coefficients is also considered. The denoising results confirm the effectiveness of the proposed method.

Regularized Least Square Approach for Remote Sensing Image Denoising using Wavelet Filters

Noise in remote sensing images (aerial and satellite) is caused due to various reasons such as atmospheric interference or lack of quality in sensors used to capture them. Removal of noise in an efficient way is a big challenge for researchers. In this paper, one dimensional signal denoising based on weighted regularized least square method is mapped to two dimensional image de noising. Objectives: This paper introduces a novel image denoising technique based on least square weighted regularization. Methods/Statistical Analysis: The proposed technique for image denoising based on Least Square (LS) approach is experimented on five different satellite and aerial images corrupted by gaussian noise with varying noise levels and regularization parameter lambda (λ) for different wavelet filter coefficients such as ‘haar’, ‘symlet’, ‘daubechies’ and coiflet. The effectiveness of the proposed method of image denoising is compared against the existing second order filter [based on LS] and conventional wavelet based image denoising technique based on the standard metric called Peak Signal to Noise Ratio (PSNR). Findings: From the experimental result analysis obtained it is inferred that the wavelet filters outperforms the second order filter and the conventional wavelet based image denoising. The complexity of the mathematics is low in our proposed method for image denoising. Applications/Improvements: The proposed denoising technique can be adopted as a faster pre-processing step in most of the image processing applications.

Gap Measurement of Point Machine Using Adaptive Wavelet Threshold and Mathematical Morphology.

A point machine’s gap is an important indication of its healthy status. An edge detection algorithm is proposed to measure and calculate a point machine’s gap from the gap image captured by CCD plane arrays. This algorithm integrates adaptive wavelet-based image denoising, locally adaptive image binarization, and mathematical morphology technologies. The adaptive wavelet-based image denoising obtains not only an optimal denoising threshold, but also unblurred edges. Locally adaptive image binarization has the advantage of overcoming the local intensity variation in gap images. Mathematical morphology may suppress speckle spots caused by reflective metal surfaces in point machines. The subjective and objective evaluations of the proposed method are presented by using point machine gap images from a railway corporation in China. The performance between the proposed method and conventional edge detection methods has also been compared, and the result shows that the former outperforms the latter.

Block compressed sensing reconstruction with adaptive-thresholding projected Landweber for aerial imagery

A block compressed sensing with projected Landweber (BCS-PL) framework that incorporates the universal measurement and projected-Landweber iterative reconstruction is summarized. Based on the BCS-PL framework, an improved reconstruction algorithm for aerial imagery: block compressed sensing with adaptive-thresholding projected Landweber (BCS-ATPL), which leverages a piecewise-linear thresholding model for wavelet-based image denoising, is presented. Through analyzing the functional relation between the thresholding factors and sampling subrates, the proposed adaptive-thresholding model can effectively remove wavelet-domain noise of bivariate shrinkage. For the reconstruction quality of aerial images, experimental results demonstrate that the proposed BCS-ATPL algorithm consistently outperforms several existing BCS-PL reconstruction algorithms. With the experiment-driven methodology, the BCS-ATPL algorithm can preserve better reconstruction quality at a competitive computational cost, which makes it more desirable for aerial imagery applications.

Wavelet-Based Medical Image Denoising and Enhancement

The visual quality of medical images is an important aspect in PACS implementation. In this study, on the basis of wavelet analysis, a denoising and enhancement algorithm for medical image is proposed. The algorithm mainly includes six steps. At first, an effcient method is investigated for Poisson Noise remove. Second, diagnosis features of the denoised image are enhanced by compressing the dynamic range. Third, we extract the high frequency component of the original image by the designed lowpass filter. Fourth, the extracted high frequency component are segment into diagnosis feature component in the high signal range, the diagnosis feature component in the low signal range, and the noise component. Five, we reconstruct an image using image fusion. Finally, we make DICOM calibration for used display and decide parameters of the image fusion, resulting in the diagnosis image. Experimental results show that this new scheme offers effective noise removal in medical images and enhancing sharpness. More importantly, this scheme can improve the diagnostic value of the display image on the commercial display successfully.

A Comparative Study on Thresholding Methods in Wavelet-based Image Denoising

Wavelet-based image denoising is an important technique in the area of image noise reduction. Wavelets have their natural ability to represent images in a very sparse form which is the foundation of wavelet-based denoising through thresholding. This paper explores properties of several representative thresholding techniques in wavelets denoising, such as VisuShrink, SureShrink, BayesShrink and Feature Adaptive Shrinkage. A quantitative comparison between these techniques through PSNR (Peak Signal-to-Noise Ratio) is also given.

Using diffusion equations for improving performance of wavelet-based image denoising techniques

A new method based on anisotropic diffusion and wavelet transform is presented for image noise reduction. In the existing wavelet thresholding methods, the final noise reduced image has limited improvement. It is due to keeping the approximate coefficients of the image unchanged. These coefficients have the main information of the image. Since noise affects both the approximate and detail coefficients, in this research, the anisotropic diffusion technique for noise reduction is applied on the approximation band to alleviate the deficiency of the existing wavelet thresholding methods. The proposed method was applied on several standard noisy images and the results indicate superiority of the proposed method over the existing wavelet-based image denoising, anisotropic diffusion, fourth-order anisotropic diffusion and median filtering techniques.

A Wavelet-Based Mammographic Image Denoising and Enhancement with Homomorphic Filtering

Breast cancer continues to be a significant public health problem in the world. The diagnosing mammography method is the most effective technology for early detection of the breast cancer. However,...

Parallel implementation of wavelet-based image denoising on programmable PC-grade graphics hardware

The discrete wavelet transform (DWT) has been extensively used for image compression and denoising in the areas of image processing and computer vision. However, the intensive computation of DWT due to its inherent multilevel data decomposition and reconstruction operations brings a bottleneck that drastically reduces its performance and implementations for real-time applications when facing large size digital images and/or high-definition videos. Although various software-based acceleration solutions, such as the lifting scheme, have been devised and achieved a higher performance in general, the pure software accelerated DWT still struggle to cope with the demands from real-time and interactive applications. With the growing capacity and popularity of graphics hardware, personal computers (PCs) nowadays are often equipped with programmable graphics processing units (GPUs) for graphics acceleration. The GPU offers a cost-effective parallel data processing mechanism for operations on large amount of data, even for applications beyond graphics. This practice is commonly referred as general-purpose computing on GPU (GPGPU). This paper presented a GPGPU framework with the corresponding parallel computing solution for wavelet-based image denoising by using off-the-shelf consumer-grade programmable GPUs. This framework can be readily incorporated with different forms of DWT by customizing the parameter of the wavelet kernel. Experiment results show that the framework gains applicability in data parallelism and satisfaction performance in accelerating computations for wavelet-based denoising.

The Estimation of Radial Exponential Random Vectors in Additive White Gaussian Noise

Image signals are always disturbed by noise during their transmission, such as in mobile or network communication. The received image quality is significantly influenced by noise. Thus, image signal denoising is an indispensable step during image processing. As we all know, most commonly used methods of image denoising is Bayesian wavelet transform estimators. The Performance of various estimators, such as maximum a posteriori (MAP), or minimum mean square error (MMSE) is strongly dependent on correctness of the proposed model for original data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is important in wavelet-based image denoising. This paper presents a new image denoising algorithm based on the modeling of wavelet coefficients in each subband with multivariate Radial Exponential probability density function (PDF) with local variances. Generally these multivariate extensions do not result in a closed form expression, and the solution requires numerical solutions. However, we drive a closed form MMSE shrinkage functions for a Radial Exponential random vectors in additive white Gaussian noise (AWGN). The estimator is motivated and tested on the problem of wavelet-based image denoising. In the last, proposed, the same idea is applied to the dual-tree complex wavelet transform (DT-CWT), This Transform is an over-complete wavelet transform.

The Estimation of Laplace Random Vectors in Additive White Gaussian Noise

This paper develops and compares the maximum <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">posteriori</i> (MAP) and minimum mean-square error (MMSE) estimators for spherically contoured multivariate Laplace random vectors in additive white Gaussian noise. The MMSE estimator is expressed in closed-form using the generalized incomplete gamma function. We also find a computationally efficient yet accurate approximation for the MMSE estimator. In addition, this paper develops an expression for the MSE for any estimator of spherically contoured multivariate Laplace random vectors in additive white Gaussian noise (AWGN), the development of which again depends on the generalized incomplete gamma function. The estimators are motivated and tested on the problem of wavelet-based image denoising.

An elliptically contoured exponential mixture model for wavelet based image denoising

An elliptically contoured exponential distribution is developed as a generalization of the univariate Laplacian distribution to multi-dimensions. A mixture of this model is used as the wavelet coefficient prior for Bayesian wavelet based image denoising. The mixture model has a small number of parameters yet fits the marginal distribution of wavelet coefficients well. Despite being a stationary probability model, it is able to capture the dependencies among coefficients. Efficient parameter estimation methods and denoising rules are derived for the model. Denoising results are compared with existing techniques in both PSNR values and visual quality.

Optimization of partition-based weighted sum filters and their application to image denoising

Partition-based Weighted Sum (P-WS) filtering is an effective method for processing nonstationary signals, especially those with regularly occurring structures, such as images. P-WS filters were originally formulated as Hard-partition Weighted Sum (HP-WS) filters and were successfully applied to image denoising. This formulation relied on intuitive arguments to generate the filter class. Here we present a statistical analysis that justifies the use of weighted sum filters after observation space partitioning. Unfortunately, the HP-WS filters are nondifferentiable and an analytical solution for their global optimization is therefore difficult to obtain. A two-stage suboptimal training procedure has been reported in the literature, but prior to this research no evaluation on the optimality of this approach has been reported. Here, a Genetic Algorithm (GA) HP-WS optimization procedure is developed that, in simulations, shows that the simpler two-stage training procedure yields near optimal results. Also developed in this paper are Soft-partition Weighted Sum (SP-WS) filters. The SP-WS filters utilize soft, or fuzzy, partitions that yield a differentiable filtering operation, enabling the development of gradient-based optimization procedures. Image denoising simulation results are presented comparing HP-WS and SP-WS filters, their optimization procedures, and wavelet-based image denoising. These results show that P-WS filters, in general, outperform traditional and wavelet-based image filters, and SP-WS filters utilizing soft partitioning not only allow for simple optimization, but also yields improved performance.

Wavelet based image denoising: VQ - Bayesian technique

An image denoising algorithm for the wavelet-transform domain of an image is presented. In the proposed method, a Bayesian estimation procedure is used to restore the higher scale wavelet coefficients, while vector quantisation is used to realise a spatially adaptive Bayesian estimation procedure for the lower scales. The proposed algorithm provides an improved noise suppression performance as compared to that of the denoising algorithm of Mallat and Hwang (1992) and also that of Malfait and Roose (1997).