arXiv subjects

Pablo Arratia

Publications and source records attributed to Pablo Arratia.

3 recordsLinked to original sources

arXiv2025

Neural Fields for Highly Accelerated 2D Cine Phase Contrast MRI

2D cine phase contrast (CPC) MRI provides quantitative information on blood velocity and flow within the human vasculature. However, data acquisition is time-consuming, motivating the reconstruction of the velocity field from undersampled measurements to reduce scan times. In this work, neural fields are proposed as a continuous spatiotemporal parametrization of complex-valued images, jointly modeling magnitude and phase across multiple echoes to enable velocity estimation, and leveraging their inductive bias for the reconstruction of the velocity data. Additionally, to compensate for the oversmoothing tendency observed in neural-field reconstructions under severe undersampling, a simple voxel-based postprocessing step is introduced. The method is validated numerically in Cartesian and radial k-space with both high and low temporal resolution data. This approach achieves accurate reconstructions at high acceleration factors, with low errors even at 32$\times$ and 64$\times$ undersampling for the high temporal resolution data, and 16$\times$ for the low temporal resolution data, and consistently outperforms classical locally low-rank regularized voxel-based methods in both flow estimates and anatomical depiction.

eess.IV↗

arXiv2024

Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow

In this paper, we investigate image reconstruction for dynamic Computed Tomography. The motion of the target with respect to the measurement acquisition rate leads to highly resolved in time but highly undersampled in space measurements. Such problems pose a major challenge: not accounting for the dynamics of the process leads to a poor reconstruction with non-realistic motion. Variational approaches that penalize time evolution have been proposed to relate subsequent frames and improve image quality based on classical grid-based discretizations. Neural fields have emerged as a novel way to parameterize the quantity of interest using a neural network with a low-dimensional input, benefiting from being lightweight, continuous, and biased towards smooth representations. The latter property has been exploited when solving dynamic inverse problems with neural fields by minimizing a data-fidelity term only. We investigate and show the benefits of introducing explicit motion regularizers for dynamic inverse problems based on partial differential equations, namely, the optical flow equation, for the optimization of neural fields. We compare it against its unregularized counterpart and show the improvements in the reconstruction. We also compare neural fields against a grid-based solver and show that the former outperforms the latter in terms of PSNR in this task.

eess.IV↗

arXiv2023

Lipschitz stability for Backward Heat Equation with application to Fluorescence Microscopy

This second version of the manuscript includes, in the appendices, an erratum that points out an error on the published version and offers alternative results for the Lipschitz stability analysis of the backward heat propagation problem and its applications to light sheet fluorescence microscopy. Abstract of the first version: In this work, we study a Lipschitz stability result in the reconstruction of a compactly supported initial temperature for the heat equation in $\mathbb{R}^n$, from measurements along a positive time interval and over an open set containing its support. We take advantage of the explicit dependency of solutions to the heat equation with respect to the initial condition. By means of Carleman estimates we obtain an analogous result for the case when the observation is made along an exterior region $ω\times(τ,T)$, such that the unobserved part $\mathbb{R}^n\backslashω$ is bounded. In the latter setting, the method of Carleman estimates gives a general conditional logarithmic stability result when initial temperatures belong to a certain admissible set, and without the assumption of compactness of support. Furthermore, we apply these results to deduce a similar result for the heat equation in $\mathbb{R}$ for measurements available on a curve contained in $\mathbb{R}\times [0,\infty)$, from where a stability estimate for an inverse problem arising in 2D Fluorescence Microscopy is deduced as well. In order to further understand this Lipschitz stability, in particular, the magnitude of its stability constant with respect to the noise level of the measurements, a numerical reconstruction is presented based on the construction of a linear system for the inverse problem in Fluorescence Microscopy. We investigate the stability constant with the condition number of the corresponding matrix.

math.AP↗