Related papers: Denosing Using Wavelets and Projections onto the L…
The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it…
Donoho and Johnstone proposed a method from reconstructing an unknown smooth function $u$ from noisy data $u+\zeta$ by translating the empirical wavelet coefficients of $u+\zeta$ towards zero. We consider the situation where the prior…
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…
Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost…
In [DOI:10.1109/ICMEW.2014.6890711], a graph-based denoising is performed by projecting the noisy image to a lower dimensional Krylov subspace of the graph Laplacian, constructed using nonnegative weights determined by distances between…
Convolutional neural networks (CNNs) have shown outstanding performance on image denoising with the help of large-scale datasets. Earlier methods naively trained a single CNN with many pairs of clean-noisy images. However, the conditional…
Though achieving excellent performance in some cases, current unsupervised learning methods for single image denoising usually have constraints in applications. In this paper, we propose a new approach which is more general and applicable…
Weak gravitational lensing is a very sensitive way of measuring cosmological parameters, including dark energy, and of testing current theories of gravitation. In practice, this requires exquisite measurement of the shapes of billions of…
We propose a general framework for denoising high-dimensional measurements which requires no prior on the signal, no estimate of the noise, and no clean training data. The only assumption is that the noise exhibits statistical independence…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…
We consider the Additive White Gaussian Noise channel with Binary Phase Shift Keying modulation. Our aim is to enable an algebraic hard decision Bounded Minimum Distance decoder for a binary block code to exploit soft information obtained…
The measurements of very low level signals at low frequency is a very difficult problem, because environmental noise increases in this frequency domain and it is very difficult to filter it efficiently. In order to counteract these major…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
Supervised training for real-world denoising presents challenges due to the difficulty of collecting large datasets of paired noisy and clean images. Recent methods have attempted to address this by utilizing unpaired datasets of clean and…
Image denoising is a fundamental task in low-level computer vision. While recent deep learning-based image denoising methods have achieved impressive performance, they are black-box models and the underlying denoising principle remains…
In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…
This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…
Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using…
Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…
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…