This paper presents a novel wavelet-based image denoising algorithm under overcomplete expansion. In order to optimize the denoising performance, we make a systematic study of both signal and noise characteristics under overcomplete expansion. Highband coefficients are viewed as the mixture of non-edge class and edge class observing different probability models. Based on improved statistical mo...

Wavelet based image denoising is an important technique in the area of image noise reduction. In this paper, a new adaptive wavelet based image denoising algorithm in the presence of Gaussian noise is developed. In the existing wavelet thresholding methods, the final noise reduced image has limited improvement. It is due to keeping the approximate wavelet coefficients unchanged. Since noise aff...

PURPOSE To investigate four-dimensional flow denoising using the divergence-free wavelet (DFW) transform and compare its performance with existing techniques. THEORY AND METHODS DFW is a vector-wavelet that provides a sparse representation of flow in a generally divergence-free field and can be used to enforce "soft" divergence-free conditions when discretization and partial voluming result i...

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...

Denoising of Positron Emission Tomography (PET) images is a challenging task due to the inherent low signal-to-noise ratio (SNR) of the acquired data. A pre-processing denoising step may facilitate and improve the results of further steps such as segmentation, quantification or textural features characterization. Different recent denoising techniques have been introduced and most state-of-the-a...

The sparseness and decorrelation properties of the discrete wavelet transform have been exploited to develop powerful denoising methods. However, most of these methods have free parameters which have to be adjusted or estimated. In this paper, we propose a wavelet-based denoising technique without any free parameters; it is, in this sense, a "universal" method. Our approach uses empirical Bayes...

Variational methods are very common in image processing. They are used for denoising, deblurring, segmentation or inpainting. In this short paper we review a method for the solution of a special class of variational problems, presented in [2]. We show applications to TV denoising and new applications to total variation deblurring, wavelet shrinkage and texture extraction. Moreover this approach...

The aim of this study was to investigate the application of wavelet denoising in noise reduction of multichannel high resolution ECG signals. In particular, the influence of the selection of wavelet function and the choice of decomposition level on efficiency of denoising process were considered and whole procedures of noise reduction were implemented in MatLab environment. The Fast Wavelet Tra...

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only...

The sparseness and decorrelation properties of the discrete wavelet transform have been exploited to develop powerful denoising methods. Most schemes use arbitrary thresholding nonlinearities with ad hoc parameters, or employ computationally expensive adaptive procedures. We overcome these de ciencies with a new wavelet-based denoising technique derived from a simple empirical Bayes approach ba...