Related papers: Fast algorithms for hyperspectral Diffuse Optical …
Diffuse optical tomography (DOT) is a severely ill-posed nonlinear inverse problem that seeks to estimate optical parameters from boundary measurements. In the Bayesian framework, the ill-posedness is diminished by incorporating {\em a…
Light scattering imposes a major obstacle for imaging objects seated deeply in turbid media, such as biological tissues and foggy air. Diffuse optical tomography (DOT) tackles scattering by volumetrically recovering the optical absorbance…
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…
Reconstructing an image from its Radon transform is a fundamental computed tomography (CT) task arising in applications such as X-ray scans. In many practical scenarios, a full 180-degree scan is not feasible, or there is a desire to reduce…
Hyperspectral neutron computed tomography enables 3D non-destructive imaging of the spectral characteristics of materials. In traditional hyperspectral reconstruction, the data for each neutron wavelength bin is reconstructed separately.…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving…
The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging to…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
This paper deals with the problem of building fast and reliable 3D reconstruction methods for blood flows for which partial information is given by Doppler ultrasound measurements. This task is of interest in medicine since it could enrich…
In this work, we investigate the diffusive optical tomography (DOT) problem in the case that limited boundary measurements are available. Motivated by the direct sampling method (DSM), we develop a deep direct sampling method (DDSM) to…
The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of the operators can be constructed by using FFT, if data is…
Score-based diffusion models have significantly advanced generative deep learning for image processing. Measurement conditioned models have also been applied to inverse problems such as CT reconstruction. However, the conventional approach,…
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,…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
Light scattering by tissue severely limits how deep beneath the surface one can image, and the spatial resolution one can obtain from these images. Diffuse optical tomography (DOT) is one of the most powerful techniques for imaging deep…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
In many ultrasonic imaging systems, data acquisition and image formation are performed on separate computing devices. Data transmission is becoming a bottleneck, thus, efficient data compression is essential. Compression rates can be…