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We propose a patch-based singular value shrinkage method for diffusion magnetic resonance image estimation targeted at low signal to noise ratio and accelerated acquisitions. It operates on the complex data resulting from a sensitivity…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…
This paper proves a novel analytical inversion formula for the so-called modulo Radon transform (MRT), which models a recently proposed approach to one-shot high dynamic range tomography. It is based on the solution of a Poisson problem…
Speed-of-sound is a biomechanical property for quantitative tissue differentiation, with great potential as a new ultrasound-based image modality. A conventional ultrasound array transducer can be used together with an acoustic mirror, or…
In view synthesis, a neural radiance field approximates underlying density and radiance fields based on a sparse set of scene pictures. To generate a pixel of a novel view, it marches a ray through the pixel and computes a weighted sum of…
X-ray computed tomography (XCT) is an important tool for high-resolution non-destructive characterization of additively-manufactured metal components. XCT reconstructions of metal components may have beam hardening artifacts such as cupping…
Recently, generative diffusion priors have made huge strides as inverse problem solvers, including the ability to be adapted for inference on out-of-distribution data. Concurrently, implicit neural representations (INRs) have emerged as…
We consider a wide class of generalized Radon transforms $\mathcal R$, which act in $\mathbb{R}^n$ for any $n\ge 2$ and integrate over submanifolds of any codimension $N$, $1\le N\le n-1$. Also, we allow for a fairly general reconstruction…
Relative radiometric normalization(RRN) of different satellite images of the same terrain is necessary for change detection, object classification/segmentation, and map-making tasks. However, traditional RRN models are not robust,…
This article presents original work combining a NURBS-based inverse analysis with both kinematic and constitutive nonlinearities to recover the applied loads and deformations of thin shell structures. The inverse formulation is tackled by…
We introduce bendlets, a shearlet-like system that is based on anisotropic scaling, translation, shearing, and bending of a compactly supported generator. With shearing being linear and bending quadratic in spatial coordinates, bendlets…
An efficient and accurate image reconstruction algorithm for ultrasound tomography (UST) is described and demonstrated, which can recover accurate sound speed distribution from acoustic time series measurements made in soft tissue. The…
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner…
Tomographic investigations are a central tool in medical applications, allowing doctors to image the interior of patients. The corresponding measurement process is commonly modeled by the Radon transform. In practice, the solution of the…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
Invertible networks have various benefits for image denoising since they are lightweight, information-lossless, and memory-saving during back-propagation. However, applying invertible models to remove noise is challenging because the input…
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…
The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper, we investigate this issue for the sparse data problem in photoacoustic tomography (PAT). We develop a direct and…
Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…
Convolutional Neural Networks (CNNs) perform very well in image classification and object detection in recent years, but even the most advanced models have limited rotation invariance. Known solutions include the enhancement of training…