Product of Gaussian Mixture Diffusion Models

In this work we tackle the problem of estimating the density $f_X$ of a random variable $X$ by successive smoothing, such that the smoothed random variable $Y$ fulfills the diffusion partial differential equation $(\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0$ with initial condition $f_Y(\,\cdot\,, 0) = f_X$. We propose a product-of-experts-type model utilizing Gaussian mixture experts and study configurations that admit an analytic expression for $f_Y (\,\cdot\,, t)$. In particular, with a focus on image processing, we derive conditions for models acting on filter-, wavelet-, and shearlet responses. Our construction naturally allows the model to be trained simultaneously over the entire diffusion horizon using empirical Bayes. We show numerical results for image denoising where our models are competitive while being tractable, interpretable, and having only a small number of learnable parameters. As a byproduct, our models can be used for reliable noise estimation, allowing blind denoising of images corrupted by heteroscedastic noise

Speckle Noise Reduction in Medical Ultrasound Images Using Modelling of Shearlet Coefficients as a Nakagami Prior

The diagnosis of UltraSound (US) medical images is affected due to the presence of speckle noise. This noise degrades the diagnostic quality of US images by reducing small details and edges present in the image. This paper presents a novel method based on shearlet coefficients modeling of log-transformed US images. Noise-free log-transformed coefficients are modeled as Nakagami distribution and speckle noise coefficients are modeled as Gaussian distribution. Method of Log Cumulants (MoLC) and Method of Moments (MoM) are used for parameter estimation of Nakagami distribution and noise free shearlet coefficients respectively. Then noise free shearlet coefficients are obtained using Maximum a Posteriori (MaP) estimation of noisy coefficients. The experimental results were presented by performing various experiments on synthetic and real US images. Subjective and objective quality assessment of the proposed method is presented and is compared with six other existing methods. The effectiveness of the proposed method over other methods can be seen from the obtained results

Effective SAR image despeckling based on bandlet and SRAD

Despeckling of a SAR image without losing features of the image is a daring task as it is intrinsically affected by multiplicative noise called speckle. This thesis proposes a novel technique to efficiently despeckle SAR images. Using an SRAD filter, a Bandlet transform based filter and a Guided filter, the speckle noise in SAR images is removed without losing the features in it. Here a SAR image input is given parallel to both SRAD and Bandlet transform based filters. The SRAD filter despeckles the SAR image and the despeckled output image is used as a reference image for the guided filter. In the Bandlet transform based despeckling scheme, the input SAR image is first decomposed using the bandlet transform. Then the coefficients obtained are thresholded using a soft thresholding rule. All coefficients other than the low-frequency ones are so adjusted. The generalized cross-validation (GCV) technique is employed here to find the most favorable threshold for each subband. The bandlet transform is able to extract edges and fine features in the image because it finds the direction where the function gives maximum value and in the same direction it builds extended orthogonal vectors. Simple soft thresholding using an optimum threshold despeckles the input SAR image. The guided filter with the help of a reference image removes the remaining speckle from the bandlet transform output. In terms of numerical and visual quality, the proposed filtering scheme surpasses the available despeckling schemes

Review on Colour Image Denoising using Wavelet Soft Thresholding Technique

In this modern age of communication the image and video is important as Visual information transmitted in the form of digital images, but after the transmission image is often ruined with noise. Therefore the received image needs to be processing before it can be used for further applications. Image denoising implicates the manipulation of the image data to produce a high quality of image without any noise. Most of the work which had done in color scale image is by filter domain approach, but we think that the transform domain approach give great result in the field of color image denoising.. This paper reviews the several types of noise which corrupted the color image and also the existing denoising algorithms based on wavelet threshodling technique. DOI: 10.17762/ijritcc2321-8169.15039

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)

Despeckling Of Synthetic Aperture Radar Images Using Shearlet Transform

Synthetic Aperture Radar (SAR) is widely used for producing high quality imaging of Earth sur- face due to its capability of image acquisition in all- weather conditions. However, one limitation of SAR image is that image textures and fine details are usually contaminated with multiplicative granular noise named as speckle noise. This paper presents a speckle reduc- tion technique for SAR images based on statistical mod- elling of detail band shearlet coefficients (SC) in ho- momorphic environment. Modelling of SC correspond- ing to noiseless SAR image are carried out as Nor- mal Inverse Gaussian (NIG) distribution while speckle noise SC are modelled as Gaussian distribution. These SC are segmented as heterogeneous, strongly hetero- geneous and homogeneous regions depending upon the local statistics of images. Then maximum a posteri- ori (MAP) estimation is employed over SC that belong to homogenous and heterogenous region category. The performance of proposed method is compared with seven other methods based on objective and subjective quality measures. PSNR and SSIM metrics are used for objec- tive assessment of synthetic images and ENL metric is used for real SAR images. Subjective assessment is carried out by visualizing denoised images obtained from various methods. The comparative result analy- sis shows that for the proposed method, higher values of PSNR i.e. 26.08 dB, 25.39 dB and 23.82 dB and SSIM i.e. 0.81, 0.69 and 0.61 are obtained for Barbara im- age at noise variances 0.04, 0.1 and 0.15, respectively as compared to other methods. For other images also results obtained for proposed method are at higher side. Also, ENL for real SAR images show highest average value of 125.91 79.05. Hence, the proposed method sig- nifies its potential in comparison to other seven existing image denoising methods in terms of speckle denoising and edge preservation