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In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…
In this paper, we introduced a novel deep learning-based reconstruction technique for low-dose CT imaging using 3 dimensional convolutions to include the sagittal information unlike the existing 2 dimensional networks which exploits…
In this work, we present a novel self-supervised method for Low Dose Computed Tomography (LDCT) reconstruction. Reducing the radiation dose to patients during a CT scan is a crucial challenge since the quality of the reconstruction highly…
We reconstruct a closed denoised curve from an unstructured and highly noisy 2D point cloud. Our proposed method uses a two- pass approach: Previously recovered manifold connectivity is used for ordering noisy samples along this manifold…
Conventional MRI reconstruction methods treat images and coil sensitivities as discrete objects, leading to high memory demands and limited structural awareness that hamper effective regularization. These limitations hinder accurate…
Low-light image enhancement is a classical computer vision problem aiming to recover normal-exposure images from low-light images. However, convolutional neural networks commonly used in this field are good at sampling low-frequency local…
Limited-angle computed tomography (LACT) reconstruction is an inverse problem with severe ill-posedness arising from missing projection angles, and it is difficult to restore high-precision images without sufficient prior knowledge. In…
Magnetic resonance electrical impedance tomography (MREIT) aims to recover the electrical conductivity distribution of an object using partial information of magnetic flux densities inside the tissue which can be measured using an MRI…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
In this paper, we present a fast divergence-free spectral algorithm (FDSA) for the curl-curl problem. Divergence-free bases in two and three dimensions are constructed by using the generalized Jacobi polynomials. An accurate spectral method…
This paper presents novel single and multi-shell sampling schemes for diffusion MRI. In diffusion MRI, it is paramount that the number of samples is as small as possible in order that scan times are practical in a clinical setting. The…
Parallel MRI is a fast imaging technique that enables the acquisition of highly resolved images in space. It relies on $k$-space undersampling and multiple receiver coils with complementary sensitivity profiles in order to reconstruct a…
The purpose of this work is to implement physics-based regularization as a stopping condition in tuning an untrained deep neural network for reconstructing MR images from accelerated data. The ConvDecoder neural network was trained with a…
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training…
Image reconstruction from computed tomography (CT) measurement is a challenging statistical inverse problem since a high-dimensional conditional distribution needs to be estimated. Based on training data obtained from high-quality…
In this paper we study the performance of image reconstruction methods from incomplete samples of the 2D discrete Fourier transform. Inspired by requirements in parallel MRI, we focus on a special sampling pattern with a small number of…
Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
In this paper, the problem of Magnetic Resonance (MR) image reconstruction from partial Fourier samples has been considered. To this aim, we leverage the evidence that MR images are sparser than their zero-filled reconstructed ones from…