arXiv subjects

Toluwani Okunola

Publications and source records attributed to Toluwani Okunola.

4 recordsLinked to original sources

arXiv2026

Nonlinear RMM-GKS for Large-Scale Dynamic and Streaming Inverse Problems with Uncertain Forward Operators

Many practical imaging systems suffer from uncertainty in acquisition geometry -- such as projection angles in computed tomography or sensor positions in photoacoustic tomography -- leading to nonlinear inverse problems that require joint estimation of both the image and the forward model parameters. Standard approaches that assume a known linear forward operator fail to account for these uncertainties, resulting in significant reconstruction artifacts. We propose a nonlinear recycled majorization-minimization generalized Krylov subspace (NL-RMM-GKS) framework for large-scale inverse problems with uncertain forward operators. The method extends MM-GKS to nonlinear settings by combining majorization-minimization for nonsmooth regularization with Krylov subspace projection and subspace recycling, ensuring bounded memory usage. Two complementary formulations are developed: an alternating minimization approach that alternates between image updates and Gauss-Newton parameter estimation, and a variable projection approach that eliminates the image variable and optimizes directly over the parameters using inexact inner solves. We further introduce streaming variants that process data sequentially, enabling reconstruction from large or dynamically acquired datasets without storing the full operator. For dynamic problems, we incorporate two temporal regularization strategies -- optical flow and anisotropic total variation -- as plug-in choices within the framework. We carry out rigorous numerical experiments in fan-beam computed tomography and photoacoustic tomography to demonstrate that our proposed framework achieves high-quality reconstructions with bounded memory requirements, making it suitable for large-scale dynamic imaging problems.

math.NA↗

arXiv2026

An Efficient Cumulative Edge-Detection Method for Image Reconstruction

When reconstructing images from noisy measurements, such as in medical scans or scientific imaging, we face an inverse problem: recovering an unknown image from indirect, corrupted observations. These problems are typically ill-posed, meaning small amounts of noise can lead to inaccurate reconstructions. Regularization techniques address this by incorporating prior assumptions about the solution, such as smoothness or sparsity. However, standard methods often blur sharp edges--the boundaries between tissues or structures--losing critical detail. A powerful strategy for edge preservation is iterative reweighting, which solves a sequence of weighted subproblems with adaptively updated weights. Non-cumulative schemes derive weights from the current iterate alone and can be solved efficiently using the Recycled Majorization-Minimization Generalized Krylov Subspace method (RMM-GKS). The cumulative approach of Gazzola et al. progressively accumulates edge information across iterations, achieving superior edge preservation but at high computational cost. This work introduces CR-$\ell_q$-RMM-GKS, which combines cumulative edge detection with computational efficiency. We integrate Gazzola's cumulative weighting with RMM-GKS, which handles general $\ell_q$ penalties ($0 < q \le 2$), automatically selects regularization parameters, and recycles Krylov subspaces between iterations, reducing the nested structure to two levels. Numerical experiments in signal deblurring and tomography demonstrate that CR-$\ell_q$-RMM-GKS produces significantly sharper edge reconstructions than standard non-cumulative methods. In particular, CR-$\ell_1$-RMM-GKS outperforms both standard $\ell_1$ methods and CR-$\ell_2$-RMM-GKS, indicating that cumulative weighting and $\ell_1$ penalties are highly complementary.

math.NA↗

arXiv2025

Efficient Dynamic Image Reconstruction with motion estimation

Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous computational challenge. In this work, in addition to the use of edge-enhancing regularization of spatial features, we propose a new regularization method that incorporates a temporal model that estimates the motion of objects in time. In particular, we consider the optical flow model that simultaneously estimates the motion and provides an approximation for the desired image, and we incorporate this information into the cost functional as an additional form of temporal regularization. We propose a computationally efficient algorithm to solve the jointly regularized problem that leverages a generalized Krylov subspace method. We illustrate the effectiveness of the prescribed approach on a wide range of numerical experiments, including limited angle and single-shot computerized tomography.

math.NA↗

arXiv2023

Partial mean-field model for neurotransmission dynamics

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.

physics.bio-ph↗