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We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
Four-dimensional Scanning Transmission Electron Microscopy (4D STEM) with data acquired using a defocused electron probe is a promising tool for characterising complex biological specimens and materials through a phase retrieval process…
We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…
In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In…
Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points $\boldsymbol{\gamma} \subset P$, are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental…
Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny…
Lossy image compression is a many-to-one process, thus one bitstream corresponds to multiple possible original images, especially at low bit rates. However, this nature was seldom considered in previous studies on image compression, which…
While many graph drawing algorithms consider nodes as points, graph visualization tools often represent them as shapes. These shapes support the display of information such as labels or encode various data with size or color. However, they…
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…
The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…
Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…
Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner,…