Related papers: Solution of linear ill-posed problems using random…

Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a…

Reverse Dictionary (RD) is the task of obtaining the most relevant word or set of words given a textual description or dictionary definition. Effective RD methods have applications in accessibility, translation or writing support systems.…

Most existing algorithms for dictionary learning assume that all entries of the (high-dimensional) input data are fully observed. However, in several practical applications (such as hyper-spectral imaging or blood glucose monitoring), only…

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…

This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to…

We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…

We tackle the problem of recovering an unknown signal observed in an ill-posed inverse problem framework. More precisely, we study a procedure commonly used in numerical analysis or image deblurring: minimizing an empirical loss function…

We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…

The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…

In this paper we consider inverse problems that are mathematically ill-posed. That is, given some (noisy) data, there is more than one solution that approximately fits the data. In recent years, deep neural techniques that find the most…

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…

This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…

The analysis of linear ill-posed problems often is carried out in function spaces using tools from functional analysis. However, the numerical solution of these problems typically is computed by first discretizing the problem and then…

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…

Recently, great attention was intended toward overcomplete dictionaries and the sparse representations they can provide. In a wide variety of signal processing problems, sparsity serves a crucial property leading to high performance.…

In this paper, we apply randomized algorithms to approximate the total least squares (TLS) solution of the problem $Ax\approx b$ in the large-scale discrete ill-posed problems. A regularization technique, based on the multiplicative…

This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and…

Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…