Related papers: Learning phase diversity for solving ill-posed inv…

The rapid progress in machine learning methods has been empowered by i) huge datasets that have been collected and annotated, ii) improved engineering (e.g. data pre-processing/normalization). The existing datasets typically include several…

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…

Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…

We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…

Machine learning is attracting surging interest across nearly all scientific areas by enabling the analysis of large datasets and the extraction of scientific information from incomplete data. Data-driven science is rapidly growing,…

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…

Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…

Generating multi-contrasts/modal MRI of the same anatomy enriches diagnostic information but is limited in practice due to excessive data acquisition time. In this paper, we propose a novel deep-learning model for joint reconstruction and…

Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in…

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…

Sample-induced aberrations and optical imperfections limit the resolution of fluorescence microscopy. Phase diversity is a powerful technique that leverages complementary phase information in sequentially acquired images with deliberately…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

We propose neural network layers that explicitly combine frequency and image feature representations and show that they can be used as a versatile building block for reconstruction from frequency space data. Our work is motivated by the…

Super-resolution reconstruction techniques entail the utilization of software algorithms to transform one or more sets of low-resolution images captured from the same scene into high-resolution images. In recent years, considerable…

An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…

One of the primary sources of suboptimal image quality in ultrasound imaging is phase aberration. It is caused by spatial changes in sound speed over a heterogeneous medium, which disturbs the transmitted waves and prevents coherent…

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…