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Deep convolutional neural networks (CNNs) have recently achieved great success for single image super-resolution (SISR) task due to their powerful feature representation capabilities. The most recent deep learning based SISR methods focus…

Object segmentation and structure localization are important steps in automated image analysis pipelines for microscopy images. We present a convolution neural network (CNN) based deep learning architecture for segmentation of objects in…

In recent years, deep learning-based methods have been proposed for solving inverse scattering problems (ISPs), but most of them heavily rely on data and suffer from limited generalization capabilities. In this paper, a new solving scheme…

Single-Photon Emission Computed Tomography (SPECT) is widely applied for the diagnosis of ischemic heart diseases. Low-dose (LD) SPECT aims to minimize radiation exposure but leads to increased image noise. Limited-angle (LA) SPECT enables…

A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator…

In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the…

Convolutional Neural Networks (CNNs) have become indispensable for solving machine learning tasks in speech recognition, computer vision, and other areas that involve high-dimensional data. A CNN filters the input feature using a network…

Deep-neural-network-based image reconstruction has demonstrated promising performance in medical imaging for under-sampled and low-dose scenarios. However, it requires large amount of memory and extensive time for the training. It is…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

Deep learning based solutions are being succesfully implemented for a wide variety of applications. Most notably, clinical use-cases have gained an increased interest and have been the main driver behind some of the cutting-edge data-driven…

Solving inverse problems is a fundamental component of science, engineering and mathematics. With the advent of deep learning, deep neural networks have significant potential to outperform existing state-of-the-art, model-based methods for…

Inspired by certain optimization solvers, the deep unfolding network (DUN) has attracted much attention in recent years for image compressed sensing (CS). However, there still exist the following two issues: 1) In existing DUNs, most…

Supernovae Ia (SNe) can provide a unique window on the large scale structure (LSS) of the Universe at redshifts where few other observations are available, by solving the inversion problem (IP) consisting in reconstructing the LSS from its…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…

The optimization inspired network can bridge convex optimization and neural networks in Compressive Sensing (CS) reconstruction of natural image, like ISTA-Net+, which mapping optimization algorithm: iterative shrinkage-thresholding…

In this paper, we revisit the class of iterative shrinkage-thresholding algorithms (ISTA) for solving the linear inverse problem with sparse representation, which arises in signal and image processing. It is shown in the numerical…

Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural…

We introduce the Convolutional Set Transformer (CST), a novel neural architecture designed to process image sets of arbitrary cardinality that are visually heterogeneous yet share high-level semantics - such as a common category, scene, or…

We consider ill-posed inverse problems where the forward operator $T$ is unknown, and instead we have access to training data consisting of functions $f_i$ and their noisy images $Tf_i$. This is a practically relevant and challenging…

Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and…