In recent years wavelet shrinkage denoising has become the method of choice for the denoising of images. However, despite much research a number of questions remain. Which of the many wavelets that exist should one use? How should the threshold be set? and How are features in the image affected by the thresholding operation? This paper explores these issues and argues for the use of non-orthogo...

A fast, low-complexity, algorithm for solving the `1-regularized least-squares problem is devised and analyzed. Our algorithm, which we call the Inertial Iterative Soft-Thresholding Algorithm (I-ISTA), incorporates inertia into a forward-backward proximal splitting framework. We show that I-ISTA has a linear rate of convergence with a smaller asymptotic error constant than the well-known Iterat...

Wavelet shrinkage is a novel method for data denoising and function estimation. M uller and Vidakovic (1995) propose a hierarchical prior on the wavelet coeecients and shrink them by applying the induced Bayes rule. In this paper, a diierent and more elastic hierarchical prior is elicited on the model parameters describing the wavelet coeecients. Exact Bayesian analysis is impossible and the sh...

Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. In this article, we show how sparse coding can be used for denoising. Using maximum likelihood e...

Abstract In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of sum two monotone operators in real Hilbert spaces. We suggest and analyze under some mild appropriate conditions imposed on parameters such that another strong convergence theorem these is obtained. also apply our main result to improve fast shrin...

Abstract Aiming at the lack of sufficient meteorological data for runoff prediction in areas with few data, accuracy is improved by using soft thresholding under deep attention mechanism, and a residual shrinkage long-short memory network model constructed combined watershed characteristic data. The validated 134 watersheds spatial correlations CAMELS dataset. According to experimental findings...

This paper presents an approach which addresses both de-noising and contrast enhancement. In a multiscale wavelet analysis framework, we take advantage of both soft thresholding and hard thresholding wavelet shrinkage techniques to reduce noise. In addition, we carry out nonlinear processing to enhance contrast within structures and along boundaries. Feature restoration and enhancement are acco...

Introduction In fast MR imaging, reconstruction artifacts due to undersampled k-space can be greatly reduced by applying proper nonlinear reconstructions [1] based on image-sparsifying transforms. While state-of-the-art methods rely on total variation (TV), in this paper we propose to use wavelets instead, along with a very fast algorithm. Simulations and experimental results show our ability t...