Both wavelet denoising and denosing methods using the concept of sparsity are based on softthresholding. In sparsity based denoising methods, it is assumed that the original signal is sparse in some transform domains such as the wavelet domain and the wavelet subsignals of the noisy signal are projected onto `1-balls to reduce noise. In this lecture note, it is shown that the size of the `1-bal...

Removal of noise is an essential and challengeable operation in image processing. Before performing any process, images must be first restored. Images may be corrupted by noise during image transmission through electronic media. Noise effect always corrupts any recorded image which is much more harmful for future process. To overcome the problem of noise level in digital images present a review...

Both wavelet denoising and denoising methods using the concept of sparsity are based on softthresholding. In sparsity-based denoising methods, it is assumed that the original signal is sparse in some transform domains such as the Fourier, DCT, and/or wavelet domain. The transfer domain coefficients of the noisy signal are projected onto `1-balls to reduce noise. In this lecture note, we establi...

In this paperthe eflcient implementation of different types of orthogonal wavelet transforms with respect to practical applications is discussed. Orthogonal singlewuvelet triinsfornis being based on one scaling function and one wavelet function are used for denosing of signals. Orthogonal multiwavelets are bused on several scaling filnctions and several wavelets. Since they allow properties lik...

Medical images are often corrupted by random noise due to various acquisitions, transmission, storage and display devices. Noise can seriously affect the quality of disease diagnosis or treatment. Image denosing is then a required task to ensure the quality of medical image analysis. In this paper, we propose a novel method for reducing some types of common noises in medical images by using a s...

There are mainly two types of errors existed in monitoring displacement of a rock slope: gross errors and random errors. Monitoring data is very important for the safety construction and operation of the Hydropower Station. The use of slope monitoring data for safety evaluation is influenced by the gross errors during the monitoring process. This paper presents a gross error denosing method for...

Traditional Total Variation algorithms often ignore the images edge direction. In order to make up for the flaw of the algorithm existing , a novel denosing method based on direction Total Variation is introduced, on the basis of the combination of the gradient magnitude and orientation. Firstly, the pixels are divided into edge regions and non-edge regions by gradient magnitude. Secondly, the ...

Nonparametric regression has been popularly used in curve fitting, signal denosing, and image processing. In such applications, the underlying functions (or signals) may vary irregularly, and it is very common that data are contaminated with outliers. Adaptive and robust techniques are needed to extract clean and accurate information. In this paper, we develop adaptive nonparametric M-regressio...