Related papers: Coupled regularization with multiple data discrepa…

Recovering a function or high-dimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel…

In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…

Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…

Cross-modal retrieval is the task of retrieving samples of a given modality by using queries of a different one. Due to the wide range of practical applications, the problem has been mainly focused on the vision and language case, e.g. text…

In the last years, the design of image reconstruction methods in the field of quantitative Magnetic Resonance Imaging (qMRI) has experienced a paradigm shift. Often, when dealing with (quantitative) MR image reconstruction problems, one is…

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…

Discontinuity with respect to data perturbations is common in algebraic computation where solutions are often highly sensitive. Such problems can be modeled as solving systems of equations at given data parameters. By appending auxiliary…

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…

It is commonly believed that optimizing the reverse KL divergence results in "mode seeking", while optimizing forward KL results in "mass covering", with the latter being preferred if the goal is to sample from multiple diverse modes. We…

Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to…

The reconstruction of images from measured data is an increasing field of research. For highly under-determined problems, template-based image reconstruction provides a way of compensating for the lack of sufficient data. A caveat of this…

We investigate composed image retrieval with text feedback. Users gradually look for the target of interest by moving from coarse to fine-grained feedback. However, existing methods merely focus on the latter, i.e., fine-grained search, by…

We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…

The use of simultaneous sources in geophysical inverse problems has revolutionized the ability to deal with large scale data sets that are obtained from multiple source experiments. However, the technique breaks when the data has…

This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…

The conventional way of formulating inverse problems such as identification of a (possibly infinite dimensional) parameter, is via some forward operator, which is the concatenation of the observation operator with the parameter-to-state-map…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Kernel fusion is a popular and effective approach for combining multiple features that characterize different aspects of data. Traditional approaches for Multiple Kernel Learning (MKL) attempt to learn the parameters for combining the…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

Vine pair-copula constructions exist for a mix of continuous and ordinal variables. In some steps, this can involve estimating a bivariate copula for a pair of mixed continuous-ordinal variables. To assess the adequacy of copula fits for…