Related papers: Group Symmetry Enables Faster Optimization in Inve…

Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems,…

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…

The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…

Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying…

In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…

We develop a generalized inverse optimization framework for fitting the cost vector of a single linear optimization problem given multiple observed decisions. This setting is motivated by ensemble learning, where building consensus from…

The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…

In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…

Recent improvements in generative adversarial visual synthesis incorporate real and fake image transformation in a self-supervised setting, leading to increased stability and perceptual fidelity. However, these approaches typically involve…

Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…

In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…

We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets. The software package, called SetIntersectionProjection, is intended for the regularization of inverse…

We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…

Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…

Many recent applications in machine learning and data fitting call for the algorithmic solution of structured smooth convex optimization problems. Although the gradient descent method is a natural choice for this task, it requires exact…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…

Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…