Noise-free Coefficients Research Articles

SWM-DE: Statistical wavelet model for joint denoising and enhancement for multimodal medical images

Medical images are usually degraded by numerous noises during acquisition or transmission, which often causes low contrast leading to deterioration of image quality. As such, medical image denoising and enhancement has become a paramount routine task. To overcome this problem, we propose a cutting-edge joint statistical and morphological model for the denoising and enhancement operation. Firstly, we propose a statistical model in formulating the marginal distribution of the wavelet coefficients. This model is integrated into a Bayesian inference framework to develop a maximum a posterior (MAP) estimator of the noise-free coefficient. Based on the statistical model, we eliminate the need for noise level estimation, and allows the model to automatically adapts to the observed image data. Secondly, we propose an adjustable morphological reconstruction model to eliminate known and unknown noises associated with medical images, while preserving the image details. After these operations, the image is decomposed into several wavelet subbands to extract the illumination and detail components. The image is then reconstructed based on the inverse wavelet to generate the enhanced noise-free image.Experimental results show that the proposed framework obtained high EME values of 41.04, 48.81, 47.81, and 45.75 for OCTA, FFA, CT, and X-ray imaging modalities, and performs better than the state-of-the-art methods. The proposed algorithm can effectively and efficiently enhance medical images, which will assist the clinicians in disease diagnosis, monitoring, and treatment.

Image denoising in undecimated dual-tree complex wavelet domain using multivariate t-distribution

Denoising of natural images is a basic problem in image processing. The present paper proposes a new algorithm for image denoising based on the maximum a-posteriori (MAP) estimator in undecimated dual-tree complex wavelet transform. The undecimated dual-tree complex wavelet transform (UDT-CWT), along with the directional selectivity of the dual-tree complex wavelet transform (DT-CWT), offers exact translational invariance property through removing the down-sampling of filter outputs together with the up-sampling of the complex filter pairs of DT-CWT. These properties are very important in image denoising. The performance of the MAP estimator depends strongly on the probability of noise-free wavelet coefficients. In our proposed denoising method, multivariate t-distribution is applied as the prior probability of noise-free coefficients. The t-distribution can accurately model the statistics of wavelet coefficients, which have peaky and heavy-tailed characteristics. On the other hand, the multivariate model makes it possible to take into account the dependencies of wavelet coefficients and their neighbors. Also, in our work, the necessary parameters of the multivariate distribution will be estimated in a locally-adaptive way to improve the denoising results via using the correlations among the amplitudes of neighbor coefficients. Simulation results delineate that the proposed algorithm outperforms state-of-the-art denoising algorithms in the literature.

Multimodal Neuroimaging Fusion in Nonsubsampled Shearlet Domain Using Location-Scale Distribution by Maximizing the High Frequency Subband Energy

A fusion of medical imaging data obtained from different modalities plays an important role in the current clinical practice. In this paper, we propose a novel multimodal fusion algorithm for brain imaging data based on the statistical properties of nonsubsampled shearlet transform (NSST) coefficients and a novel energy maximization fusion rule. The marginal distributions of the high-frequency NSST coefficients exhibit heavier tails than the Gaussian distribution. As a consequence, after studying its characteristics, we use a heavy-tailed probability density function, student’s $t$ location-scale distribution, to describe the highly non-Gaussian statistics of empirical NSST coefficients by learning the parameters using maximum likelihood estimation. Then, we employ this model to develop a maximum a posteriori estimator to obtain the noise-free coefficients. Then, for the first time, a novel fusion rule for obtaining the fused NSST coefficients based on maximizing the energy in the high-frequency subbands is proposed. Experiments are carried out on fusing two or more multimodal neuroimages taken from the BrainWeb, Alzheimer’s Disease Neuroimaging Initiative (ADNI), and Whole Brain Atlas databases. It is seen from the subjective and objective results that the proposed multimodal neuroimaging fusion method significantly outperforms the state-of-the-art methods including under noisy scenarios, and hence, it is more robust. It is also observed that the signal intensities in the fused images are better enhanced when a more number of source images are being fused. The proposed technique should benefit the medical professionals in diagnosing neurological disorders, such as Alzheimer, epilepsy, and multiple sclerosis.

Two-stage image denoising considering interscale and intrascale dependencies

A solution to the problem of reducing the noise of grayscale images is presented. To consider the intrascale and interscale dependencies, this study makes use of a model. It is shown that the dependency between a wavelet coefficient and its predecessors can be modeled by the first-order Markov chain, which means that the parent conveys all of the information necessary for efficient estimation. Using this fact, the proposed method employs the Kalman filter in the wavelet domain for image denoising. The proposed method has two stages. The first stage employs a simple denoising algorithm to provide the noise-free image, by which the parameters of the model such as state transition matrix, variance of the process noise, the observation model, and the covariance of the observation noise are estimated. In the second stage, the Kalman filter is applied to the wavelet coefficients of the noisy image to estimate the noise-free coefficients. In fact, the Kalman filter is used to estimate the coefficients of high-frequency subbands from the coefficients of coarser scales and noisy observations of neighboring coefficients. In this way, both the interscale and intrascale dependencies are taken into account. Results are presented and discussed on a set of standard 8-bit grayscale images. The experimental results demonstrate that the proposed method achieves performances competitive with the state-of-the-art denoising methods in terms of both peak-signal-to-noise ratio and subjective visual quality.

Review of Various Image Restoration and Denoising Methods Underwater Images

The paper presents a denoising method, based on Daubechies Wavelet transform and filters, for underwater images. The method here adapts itself to various types of image noise as well as factor that are to be derived to estimate the noise-free coefficients. In the preference of the images in any field, a single parameter can be used to balance the preservation of relevant details against the degree of noise reduction. Edges play a important role in image representation, one effective means to enhance spatial resolution is to enhance the edges. DWT, a time-scale representation of the digital signal is obtained using digital filtering techniques. Effectiveness of this method is compared with all other techniques such as median ,wiener, bayes shrink and normal shrink methods for removing noise.This paper presents a review of some significant work in the area of denoising. We will introduce the wavelet and other filters methods with homomorphics filters multi-scale analysis framework and summarize related research work in this area.

Image denoising based on adaptive spatial segmentation and multi-scale correlation in directionlet domain

Directionlet transform DT has become popular over the last few years as an efficient image representation tool due to its fine frequency tiling and directional vanishing moments along any two directions. A novel denoising algorithm based on DT is proposed here for images corrupted with Gaussian noise. The image is first spatially segmented based on the content directionality. Then an undecimated version of DT is applied to effectively capture the directional features and edge information of these segments. The DT coefficients so obtained are then modelled using a bivariate heavy tailed Gaussian distribution and the noise free coefficients are computed using MAP estimator. By employing bivariate probability distribution, the heavy-tail behaviour of natural images is accurately modelled and the interscale properties of DT coefficients are properly exploited. In addition, the local variance parameter of the model is estimated based on classification of DT coefficients within a particular scale using context modelling. Due to this the intrascale dependency of the directionlet coefficients is also well exploited in the enhancement process. The proposed algorithm is competitive with the existing algorithms with better results in terms of output peak signal-to-noise ratio while having comparable computational complexity. It exhibits good capability to preserve edges, contours and textures especially in images with abundant high frequency contents.

SAR speckle reduction using Laplace mixture model and spatial mutual information in the directionlet domain

The reduction of multiplicative speckle noise which always complicates the human and automatic interpretation of objects is very significant for the practical applications of synthetic aperture radar (SAR) image. In this paper, a new maximum a posteriori (MAP) despeckling method based on directionlet transform is proposed. To convert the multiplicative noise into an additive one, the logarithmic transform is first applied to the SAR images. Then, the directionlet coefficients of the noise-free (or underlying backscatter) image and of the speckle noise are modeled as Laplace mixture distribution with zero-mean and Gaussian distribution, respectively. Within Bayesian framework, a MAP estimator is constructed using these assumed prior distributions. After obtaining the parameter estimates using expectation–maximization algorithm, the noise-free coefficients are estimated by a non-linear shrinkage function based on the average version of Bayesian estimator. To improve the denoising performance, we combine the intra-scale dependency in terms of mutual information with the MAP estimator to refine the estimated results. Finally, we compare the proposed algorithm with several other speckle filters applied on synthetic and actual SAR images. Experimental results show that the proposed method outperforms other filters in terms of signal-to-noise ratio, edge preservation and equivalent number of looks measures in most cases.

Lapped transform-based image denoising with the generalised Gaussian prior

We introduce a new image denoising method based on the statistical modelling of dyadic rearranged lapped transform LT coefficients. Based on Kolomogrov-Smirnov KS goodness of fit test, we have shown that the statistical distribution of the dyadic rearranged LT coefficients in a subband is best approximated by the generalised Gaussian distribution. A Bayesian minimum mean square error MMSE estimator is used to obtain the estimate of noise free coefficients, which is based on modelling the global distribution of the dyadic rearranged LT coefficients using generalised Gaussian distribution. The LT-based image denoising method with generalised Gaussian prior shows highly encouraging both objective and subjective results when compared to several well-known image denoising methods.

Spatially adaptive despeckling of SAR image using bivariate thresholding in directionlet domain

A novel spatially adaptive despeckling algorithm is presented for a synthetic aperture radar (SAR) image by taking into account the statistical interscale dependency of the directionlet transform (DT) coefficients. The DT is first computed along the dominant directions of the spatially segmented image. The signal and the noise coefficients are modelled using bivariate distributions which take into account the statistical dependence between the adjacent scale coefficients. The nonlinear threshold functions derived from the models employing a maximum a posteriori estimator are then used for estimating the noise-free coefficients. The experimental results show that the proposed method outperforms similar methods in terms of numerical and perceptual quality.

Segmentation of noisy colour images using Cauchy distribution in the complex wavelet domain

This study proposes a novel image segmentation technique for noisy colour images, in which the heavy-tailed characteristics of the image are modelled by Cauchy distributions. First, the RGB colour bands of the noisy image are decomposed into multiresolution representations using the dual-tree complex wavelet transform. For each wavelet subband, a model is built assuming that the input coefficients are contaminated with signal-independent additive white Gaussian noise. Hence, the authors derive an estimation rule in the wavelet domain to obtain the noise-free coefficients based on the bivariate Cauchy distribution. The bivariate model makes it possible to exploit the inter-scale dependencies of wavelet coefficients. Subsequently, the image is roughly segmented into textured and non-textured regions using the bivariate model parameters corresponding to the denoised coefficients. A multiscale segmentation is then applied to the resulting regions. Finally, a novel statistical region merging algorithm is introduced by measuring the Kullback-Leibler distance between the estimated Cauchy models for the neighbouring segments. The experiments demonstrate that the authors algorithm yields robust segmentation results for noisy images containing artificial or natural noise.

Wavelet-Based Noise Reduction by Joint Statistical Modeling of cDNA Microarray Images

Abstract Complementary DNA (cDNA) microarray experiments involve a large number of error-prone steps, which result in a high level of noise in the resulting red and green channel images. Removal of noise is a crucial step, since it makes further image processing easier and results in accurate gene expression measurements. The wavelet transform has shown significant success in the denoising of images including cDNA microarrays. Existing wavelet-based denoising methods process each image individually ignoring the information in the other channel. In this paper, a noise reduction technique is proposed that exploits the dependency between the wavelet transform coefficients of the two channels by using a locally-adaptive joint statistical model. The maximum a posteriori criterion is used to derive a joint estimator for the noise-free coefficients assuming suitable priors for the local variances. Significance of the proposed method is assessed by examining its effect on estimation of the log-intensity ratio. Ex...

Wavelet domain-based video noise reduction using temporal discrete cosine transform and hierarchically adapted thresholding

A novel spatio-temporal filter for video denoising, which operates entirely in the wavelet domain, is proposed. For effective noise reduction, the spatial and temporal redundancies that exist in the wavelet domain representation of a video signal are exploited. First, a 2D discrete wavelet transform is applied to the input noisy frames. This is followed by a discrete cosine transform (DCT), which is applied to the temporal subband coefficients to minimise the redundancy among the consecutive frames. The DCT transformed, noise-free coefficients in the different wavelet domain subbands for the original image sequence are modelled using a prior having a generalised Gaussian distribution. On the basis of this prior, filtering of the noisy wavelet coefficients in each subband is carried out using a new, low-complexity wavelet shrinkage method, which utilises the correlation that exists between subsequent resolution levels. Experimental results show that the proposed scheme outperforms several state-of-the-art spatio-temporal filters in terms of both the peak signal-to-noise ratio and the visual quality.

Wavelet domain-based video noise reduction using temporal discrete cosine transform and hierarchically adapted thresholding

A novel spatio-temporal filter for video denoising, which operates entirely in the wavelet domain, is proposed. For effective noise reduction, the spatial and temporal redundancies that exist in the wavelet domain representation of a video signal are exploited. First, a 2D discrete wavelet transform is applied to the input noisy frames. This is followed by a discrete cosine transform (DCT), which is applied to the temporal subband coefficients to minimise the redundancy among the consecutive frames. The DCT transformed, noise-free coefficients in the different wavelet domain subbands for the original image sequence are modelled using a prior having a generalised Gaussian distribution. On the basis of this prior, filtering of the noisy wavelet coefficients in each subband is carried out using a new, low-complexity wavelet shrinkage method, which utilises the correlation that exists between subsequent resolution levels. Experimental results show that the proposed scheme outperforms several state-of-the-art spatio-temporal filters in terms of both the peak signal-to-noise ratio and the visual quality.