Spatially adaptive wavelet thresholding with context modeling for image denoising

The method of wavelet thresholding for removing noise, or denoising, has been researched extensively due to its effectiveness and simplicity. Much of the literature has focused on developing the best uniform threshold or best basis selection. However, not much has been done to make the threshold values adaptive to the spatially changing statistics of images. Such adap- tivity can improve the wavelet thresholding performance because it allows additional local information of the image (such as the identification of smooth or edge regions) to be incorporated into the algorithm. This work proposes a spatially adaptive wavelet thresholding method based on context modeling, a common tech- nique used in image compression to adapt the coder to changing image characteristics. Each wavelet coefficient is modeled as a random variable of a generalized Gaussian distribution with an unknown parameter. Context modeling is used to estimate the parameter for each coefficient, which is then used to adapt the thresholding strategy. This spatially adaptive thresholding is ex- tended to the overcomplete wavelet expansion, which yields better results than the orthogonal transform. Experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower MSE than the best uniform thresholding with the original image assumed known

Wavelets and partial differential equations for image denoising

In this paper a wavelet based model for image de-noising is presented. Wavelet coefficients are modelled as waves that grow while dilating along scales. The model establishes a precise link between corresponding modulus maxima in the wavelet domain and then allows to predict wavelet coefficients at each scale from the first one. This property combined with the theoretical results about the characterization of singularities in the wavelet domain enables to discard noise. Significant structures of the image are well recovered while some annoying artifacts along image edges are reduced. Some experimental results show that the proposed approach outperforms the most recent and effective wavelet based denoising schemes

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

LV Volume Quantification via Spatiotemporal Analysis of Real-Time 3-D Echocardiography

This paper presents a method of four-dimensional (4-D) (3-D+Time) space-frequency analysis for directional denoising and enhancement of real-time three-dimensional (RT3D) ultrasound and quantitative measures in diagnostic cardiac ultrasound. Expansion of echocardiographic volumes is performed with complex exponential wavelet-like basis functions called brushlets. These functions offer good localization in time and frequency and decompose a signal into distinct patterns of oriented harmonics, which are invariant to intensity and contrast range. Deformable-model segmentation is carried out on denoised data after thresholding of transform coefficients. This process attenuates speckle noise while preserving cardiac structure location. The superiority of 4-D over 3-D analysis for decorrelating additive white noise and multiplicative speckle noise on a 4-D phantom volume expanding in time is demonstrated. Quantitative validation, computed for contours and volumes, is performed on in vitro balloon phantoms. Clinical applications of this spatiotemporal analysis tool are reported for six patient cases providing measures of left ventricular volumes and ejection fraction

Lv volume quantification via spatiotemporal analysis of real-time 3-d echocardiography

Abstract—This paper presents a method of four-dimensional (4-D) (3-D + Time) space–frequency analysis for directional denoising and enhancement of real-time three-dimensional (RT3D) ultrasound and quantitative measures in diagnostic cardiac ultrasound. Expansion of echocardiographic volumes is performed with complex exponential wavelet-like basis functions called brushlets. These functions offer good localization in time and frequency and decompose a signal into distinct patterns of oriented harmonics, which are invariant to intensity and contrast range. Deformable-model segmentation is carried out on denoised data after thresholding of transform coefficients. This process attenuates speckle noise while preserving cardiac structure location. The superiority of 4-D over 3-D analysis for decorrelating additive white noise and multiplicative speckle noise on a 4-D phantom volume expanding in time is demonstrated. Quantitative validation, computed for contours and volumes, is performed on in vitro balloon phantoms. Clinical applications of this spaciotemporal analysis tool are reported for six patient cases providing measures of left ventricular volumes and ejection fraction. Index Terms—Echocardiography, LV volume, spaciotemporal analysis, speckle denoising. I

Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin