Related papers: What is Wrong with End-to-End Learning for Phase R…

In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…

Phase retrieval (PR) concerns the recovery of complex phases from complex magnitudes. We identify the connection between the difficulty level and the number and variety of symmetries in PR problems. We focus on the most difficult far-field…

Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not…

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time,…

Inverse problems in imaging are typically ill-posed and are usually solved by employing regularized optimization techniques. The usage of appropriate constraints can restrict the solution space, thus making it feasible for a reconstruction…

Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…

Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…

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,…

In recent years, deep neural networks have emerged as a solution for inverse imaging problems. These networks are generally trained using pairs of images: one degraded and the other of high quality, the latter being called 'ground truth'.…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of…

Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…

Modern deep learning models are highly overparameterized, resulting in large sets of parameter configurations that yield the same outputs. A significant portion of this redundancy is explained by symmetries in the parameter…

Fringe projection profilometry (FPP) is one of the most popular three-dimensional (3D) shape measurement techniques, and has becoming more prevalently adopted in intelligent manufacturing, defect detection and some other important…

The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…

Deep metric learning aims to learn embeddings that contain semantic similarity information among data points. To learn better embeddings, methods to generate synthetic hard samples have been proposed. Existing methods of synthetic hard…

In the past few years, deep learning-based methods have demonstrated enormous success for solving inverse problems in medical imaging. In this work, we address the following question:\textit{Given a set of measurements obtained from real…

Fourier Ptychography is a recently proposed imaging technique that yields high-resolution images by computationally transcending the diffraction blur of an optical system. At the crux of this method is the phase retrieval algorithm, which…

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…