相关论文: Variational regularization of complex deautoconvol…

Super-resolution microscopes (such as STED) illuminate samples with a tiny spot, and achieve very high resolution. But structures smaller than the spot cannot be resolved in this way. Therefore, we propose a technique to solve this problem.…

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…

This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field,…

REgularization by Denoising (RED) is an attractive framework for solving inverse problems by incorporating state-of-the-art denoising algorithms as the priors. A drawback of this approach is the high computational complexity of denoisers,…

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying…

We are concerned with the recovery of $s-$sparse Wigner-D expansions in terms of $N$ Wigner-D functions. Considered as a generalization of spherical harmonics, Wigner-D functions are eigenfunctions of Laplace-Beltrami operator and form an…

Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…

We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive…

The spatial resolution of astronomical images is limited by atmospheric turbulence and diffraction in the telescope optics, resulting in blurred images. This makes it difficult to accurately measure the brightness of blended objects because…

Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…

X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector and the phase of the diffraction patterns is estimated using phase retrieval…

We give asymptotics for shifted convolutions of the form $$\sum_{n < X} \frac{\sigma_{2u}(n,\chi)\sigma_{2v}(n+k,\psi)}{n^{u+v}}$$ for nonzero complex numbers $u,v$ and nontrivial Dirichlet characters $\chi,\psi$. We use the technique of…

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

We consider abstract operator equations $Fu=y$, where $F$ is a compact linear operator between Hilbert spaces $U$ and $V$, which are function spaces on \emph{closed, finite dimensional Riemannian manifolds}, respectively. This setting is of…

Sparse regression methods have been proven effective in a wide range of signal processing problems such as image compression, speech coding, channel equalization, linear regression and classification. In this paper a new convex method of…

Single Image Super-Resolution (SISR) aims to recover a high-resolution image from a given low-resolution version of it. Video Super Resolution (VSR) targets series of given images, aiming to fuse them to create a higher resolution outcome.…

Speckle noise, inherent in synthetic aperture radar (SAR) images, degrades the performance of the various SAR image analysis tasks. Thus, speckle noise reduction is a critical preprocessing step for smoothing homogeneous regions while…

We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the…