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In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties of optimal solutions. In this work we…
Motion degradation is a central problem in Magnetic Resonance Imaging (MRI). This work addresses the problem of how to obtain higher quality, super-resolved motion-free, reconstructions from highly undersampled MRI data. In this work, we…
Inverse problems arise in many applications, especially tomographic imaging. We develop a Learned Alternating Minimization Algorithm (LAMA) to solve such problems via two-block optimization by synergizing data-driven and classical…
Scientific imaging often involves long acquisition times to obtain high-quality data, especially when probing complex, heterogeneous systems. However, reducing acquisition time to increase throughput inevitably introduces significant noise…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…
Regularization for denoising in magnetic resonance imaging (MRI) is typically achieved using convex regularization functions. Recently, deep learning techniques have been shown to provide superior denoising performance. However, this comes…
Neural network (NN) denoisers are an essential building block in many common tasks, ranging from image reconstruction to image generation. However, the success of these models is not well understood from a theoretical perspective. In this…
Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
This work is devoted to the stability/resolution analysis of several imaging functionals in complex environments. We consider both linear functionals in the wavefield as well as quadratic functionals based on wavefield correlations. Using…
Most variational forms of isogeometric analysis use highly-continuous basis functions for both trial and test spaces. For a partial differential equation with a smooth solution, isogeometric analysis with highly-continuous basis functions…
We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids.…
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An…
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…
We propose a model-based image reconstruction method for photoacoustic tomography(PAT) involving a novel form of regularization and demonstrate its ability to recover good quality images from significantly reduced size datasets. The…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
We introduce and discuss shape based models for finding the best interpolation data in compression of images with noise. The aim is to reconstruct missing regions by means of minimizing data fitting term in the $L^2$-norm between the images…
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…
In this work, we develop a novel technique for reconstructing images from projection-based nano- and microtomography. Our contribution focuses on enhancing reconstruction quality, particularly for specimen composed of homogeneous material…
This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an…