Related papers: Structured FISTA for Image Restoration
The selection of beam orientations, which is a key step in radiation treatment planning, is particularly challenging for non-coplanar radiotherapy systems due to the large number of candidate beams. In this paper, we report progress on the…
High-dimensional Kronecker-structured estimation faces a conflict between non-convex scaling ambiguities and statistical robustness. The arbitrary factor scaling distorts gradient magnitudes, rendering standard fixed-threshold robust…
Stochastic gradient descent (SGD) now acts as a fundamental part of optimization in current machine learning. Meanwhile, deep learning architectures have shown outstanding performance in a wide range of fields, such as natural language…
For a linear matrix function $f$ in $X \in \R^{m\times n}$ we consider inhomogeneous linear matrix equations $f(X) = E$ for $E \neq 0$ that have or do not have solutions. For such systems we compute optimal norm constrained solutions…
In the framework of sparsity-enforcing regularisation for linear inverse problems, we consider the minimisation of a square-root Lasso cost function. To solve this problem we devise a simple modification (called SQRT-ISTA) of the Iterative…
By forming measurement matrices with the Kronecker product of two random matrices, image encryption in computational ghost imaging is investigated. The two-dimensional images are conveniently reconstructed with the pseudo-inverse matrices…
High-Order, High-Dimension, and Sparse Tensor (HOHDST) data originates from real industrial applications, i.e., social networks, recommender systems, bio-information, and traffic information. Sparse Tensor Decomposition (STD) can project…
Inspired by their success in solving challenging inverse problems in computer vision, implicit neural representations (INRs) have been recently proposed for reconstruction in low-dose/sparse-view X-ray computed tomography (CT). An INR…
This paper explores the potential of conversion-based neuromorphic algorithms for highly accurate and energy-efficient single-snapshot multidimensional harmonic retrieval (MHR). By casting the MHR problem as a sparse recovery problem, we…
Structured illumination microscopy (SIM) is a very important super-resolution microscopy technique, which provides high speed super-resolution with about two-fold spatial resolution enhancement. Several attempts aimed at improving the…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
We address the problem of efficient sparse fixed-rank (S-FR) matrix decomposition, i.e., splitting a corrupted matrix $M$ into an uncorrupted matrix $L$ of rank $r$ and a sparse matrix of outliers $S$. Fixed-rank constraints are usually…
In this article, we propose an algorithm for approximating the action of $\varphi-$functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum…
Sparse coding is a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, that are optimal in the class of first-order methods for non-smooth, convex…
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
We present a new two-snapshot structured light illumination (SLI) reconstruction algorithm for fast image acquisition. The new algorithm, which only requires two mutually {\pi} phase-shifted raw structured images, is implemented on a…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…
State-of-the-art image reconstruction often relies on complex, highly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively…
In this paper we present a bilevel optimization scheme for the solution of a general image deblurring problem, in which a parametric variational-like approach is encapsulated within a machine learning scheme to provide a high quality…