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Lens modeling of resolved image data has advanced rapidly over the past two decades. More recently pixel-based approaches, wherein the source is reconstructed on an irregular or adaptive grid, have become popular. Generally, the source…

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…

We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…

In the past decade, sparsity-driven regularization has led to advancement of image reconstruction algorithms. Traditionally, such regularizers rely on analytical models of sparsity (e.g. total variation (TV)). However, more recent methods…

In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image…

We propose an approach to 3D reconstruction via inverse procedural modeling and investigate two variants of this approach. The first option consists in the fitting set of input parameters using a genetic algorithm. We demonstrate the…

This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated…

We design a new iterative algorithm, called REINFORCE-OPT, for solving a general type of optimization problems. This algorithm parameterizes the solution search rule and iteratively updates the parameter using a reinforcement learning (RL)…

There has been a growing interest in the use of data-driven regularizers to solve inverse problems associated with computational imaging systems. The convolutional sparse representation model has recently gained attention, driven by the…

Object reconstruction is an important task in many fields of application as it allows to generate digital representations of our physical world used as base for analysis, planning, construction, visualization or other aims. A reconstruction…

An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other…

Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

We present a data-assisted iterative regularization method for solving ill-posed inverse problems. The proposed approach, termed \texttt{IRMGL+\(\Psi\)}, integrates classical iterative techniques with a data-driven regularization term…

Recently, deep learning based methods appeared as a new paradigm for solving inverse problems. These methods empirically show excellent performance but lack of theoretical justification; in particular, no results on the regularization…

Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…

In this paper, we provide a modern synthesis of the classic inverse compositional algorithm for dense image alignment. We first discuss the assumptions made by this well-established technique, and subsequently propose to relax these…

Tomographic image reconstruction is relevant for many medical imaging modalities including X-ray, ultrasound (US) computed tomography (CT) and photoacoustics, for which the access to full angular range tomographic projections might be not…

Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…

We investigate generalized versions of the Iteratively Regularized Landweber Method, initially introduced in [Appl. Math. Optim., 38(1):45-68, 1998], to address linear and nonlinear ill-posed problems. Our approach is inspired by the…