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Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth. One challenge in PAT is image reconstruction with inadequate acoustic signals due to…

In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…

In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…

In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…

We present a new nonlinear optimization approach for the sparse reconstruction of single-photon absorption and two-photon absorption coefficients in photoacoustic tomography (PAT). This framework comprises of minimizing an objective…

Recent works demonstrate the effectiveness of diffusion models as unsupervised solvers for inverse imaging problems. Sparse-view computed tomography (CT) has greatly benefited from these advancements, achieving improved generalization…

A well-known diagnostic imaging modality, termed ultrasound tomography, was quickly developed for the detection of very small tumors whose sizes are smaller than the wavelength of the incident pressure wave without ionizing radiation,…

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…

Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…

Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

Diffusion models have demonstrated remarkable efficacy in generating high-quality samples. Existing diffusion-based image restoration algorithms exploit pre-trained diffusion models to leverage data priors, yet they still preserve elements…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

Large denoising diffusion models, such as Stable Diffusion, have been trained on billions of image-caption pairs to perform text-conditioned image generation. As a byproduct of this training, these models have acquired general knowledge…

Computed tomography (CT) involves a patient's exposure to ionizing radiation. To reduce the radiation dose, we can either lower the X-ray photon count or down-sample projection views. However, either of the ways often compromises image…

Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from incomplete or noisy measurements. Recent approaches employ diffusion models as powerful implicit priors for such…

Sparse views X-ray computed tomography has emerged as a contemporary technique to mitigate radiation dose. Because of the reduced number of projection views, traditional reconstruction methods can lead to severe artifacts. Recently,…

Limited-Angle Computed Tomography (LACT) is a non-destructive evaluation technique used in a variety of applications ranging from security to medicine. The limited angle coverage in LACT is often a dominant source of severe artifacts in the…

In recent years, a number of works have studied methods for computing the Fourier transform in sublinear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is…

The direction-of-arrival (DOA) estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors, thus it can be formulated as a sparse signal reconstruction problem and solved…