At first, this paper is concerned with wavelet-based image denoising using Bayesian technique. In conventional denoising process, the parameters of probability density function (PDF) are usually calculated from the first few moments, mean and variance. In the first part of our work, a new image denoising algorithm based on Pearson Type VII random vectors is proposed. This PDF is used because it allows higher-order moments to be incorporated into the noiseless wavelet coefficients' probabilistic model. One of the cruxes of the Bayesian image denoising algorithms is to estimate the variance of the clean image. Here, maximum a posterior (MAP) approach is employed for not only noiseless wavelet-coefficient estimation but also local observed variance acquisition. For the local observed variance estimation, the selection of noisy wavelet-coefficient model, either a Laplacian or a Gaussian distribution, is based upon the corrupted noise power where Gamma distribution is used as a prior for the variance. Evidently, our selection of prior is motivated by analytical and computational tractability. In our experiments, our proposed method gives promising denoising results with moderate complexity. Eventually, our image denoising method can be simply extended to audio/speech processing by forming matrix representation whose rows are formed by time segments of digital speech waveforms. This way, the use of our image denoising methods can be exploited to improve the performance of various audio/speech tasks, e.g., denoised enhancement of voice activity detection to capture voiced speech, significantly needed for speech coding and voice conversion applications. Moreover, one of the voice abnormality detections, called oropharyngeal dysphagia classification, is also required denoising method to improve the signal quality in elderly patients. We provide simple speech examples to demonstrate the prospects of our techniques.

In some circumstances, the performance of machine learning (ML) tasks are based on the quality of signal (data) that is processed in these tasks. Therefore, the pre-processing techniques, such as reconstruction and denoising methods, are important techniques in ML tasks. In reconstructed (estimated) method, the fused lasso algorithm with non-convex penalty function is an efficient method when the signal corrupted by additive white Gaussian noise (AWGN) is considered. Therefore, this paper proposes new shrinkage functions for non-convex penalty functions, modified arctangent and exponential models, in fused lasso formulation. A lot of works present the shrinkage function for arctangent penalty function. Unfortunately, there is no closed-form solution. The numerical solution is required for shrinkage function of this penalty function. However, the analytical solution is derived in this paper. Moreover, the shrinkage function of modified exponential penalty function is proposed. This shrinkage function obtains from simple iterative method, fixed-point algorithm. We demonstrate the proposed methods through simulations with standard one-dimensional signals contaminated by AWGN. The proposed techniques are compared with traditional estimation methods, such as total variation (TV) and wavelet denoising methods. In experimental results, our proposed methods outperform several exiting methods both visual quality and in terms of root mean square error (RMSE). In fact, the proposed methods can better preserve the feature of noise-free signal than the compared methods. The denoised signals produced by the proposed methods are less smooth than the denoised signals produced by the compared methods.

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In the digital world, artificial intelligence tools and machine learning algorithms are widely applied in analysis of medical images for identifying diseases and make diagnoses; for example, to make recognition and classification. Speckle noises affect all medical imaging systems. Therefore, reduction in corrupting speckle noises is very important, since it deteriorates the quality of the medical images and makes tasks such as recognition and classification difficult. Most existing denoising algorithms have been developed for the additive white Gaussian noise (AWGN). However, AWGN is not a speckle noise. Therefore, this work presents a novel speckle noise removal algorithm within the framework of Bayesian estimation and wavelet analysis. This research focuses on noise reduction by the Bayesian with wavelet-based method because it provides good efficiency in noise reduction and spends short time in processing. The subband decomposition of a logarithmically transformed image is best described by a family of heavy-tailed densities such as Logistic distribution. Then, this research proposes the maximum a posteriori (MAP) estimator assuming Logistic random vectors for each parent-child wavelet co-efficient of noise-free log-transformed data and log-normal density for speckle noises. Moreover, a redundant wavelet transform, i.e., the cycle-spinning method, is applied in our proposed methods. In our experiments, our proposed methods give promising denoising results.

In optical techniques, noise signal is a classical problem in medical image processing. Recently, there has been considerable interest in using the wavelet transform with Bayesian estimation as a powerful tool for recovering image from noisy data. In wavelet domain, if Bayesian estimator is used for denoising problem, the solution requires a prior knowledge about the distribution of wavelet coe±cients. Indeed, wavelet coe±cients might be better modeled by super Gaussian density. The super Gaussian density can be generated by Gaussian scale mixture (GSM). So, we present new minimum mean square error (MMSE) estimator for spherically-contoured GSM with Maxwell distribution in additive white Gaussian noise (AWGN). We compare our proposed method to current state-of-the-art method applied on standard test image and we quantify achieved performance improvement.