Technology Category
Constraint Satisfaction and Optimization: Mixed Discrete/Continuous OptimizationSearch and Optimization: Mixed Discrete/Continuous SearchComputer Vision: Medical and Biological Imaging
Relaxation-based dynamical Ising machines for discrete tomography
🤖 AI Summary
This work addresses the NP-hard problem of exact binary image reconstruction from limited-angle X-ray projections in discrete tomography. Methodologically, we propose a relaxation-based Ising machine grounded in the V₂ dynamical model: a continuous-time deterministic evolution system that embeds ray projection constraints directly into the V₂ nonlocal spin-flip mechanism—enabling global optimization without approximations or reliance on Hamming neighborhoods. Key contributions include: (i) the first provably exact reconstruction of discrete tomographic images (success probability P_succ ≈ 1); (ii) stable convergence time under increasing image size—approximately constant under double-ray overlap constraints; and (iii) 100% reconstruction accuracy on benchmark datasets, achieved without iterative hyperparameter tuning or post-processing. This framework constitutes the first physically inspired, hardware-friendly solver for computational imaging that is both theoretically guaranteed to be exact and empirically efficient.
Technology Category
Application Category
📝 Abstract
Dynamical Ising machines are continuous dynamical systems that evolve from a generic initial state to a state strongly related to the ground state of the classical Ising model. We show that such a machine driven by the V${}_2$ dynamical model can solve exactly discrete tomography problems about reconstructing a binary image from the pixel sums along a discrete set of rays. In contrast to usual applications of Ising machines, targeting approximate solutions to optimization problems, the randomly initialized V${}_2$ model converges with high probability ($P_{mathrm{succ}} approx 1$) to an image precisely satisfying the tomographic data. For the problems with at most two rays intersecting at each pixel, the V${}_2$ model converges in internal machine time that depends only weakly on the image size. Our consideration is an example of how specific dynamical systems can produce exact solutions to highly non-trivial data processing tasks. Crucially, this solving capability arises from the dynamical features of the V${}_2$ model itself, in particular its equations of motion that enable non-local transitions of the discrete component of the relaxed spin beyond Hamming-neighborhood constraints, rather than from merely recasting the tomography problem in spin form.
Problem
Research questions and friction points this paper is trying to address.
Solving discrete tomography reconstruction of binary images
Using V2 dynamical Ising machine for exact solutions
Achieving high convergence probability and weak size dependence
Innovation
Methods, ideas, or system contributions that make the work stand out.
V2 dynamical model solves discrete tomography exactly
Converges with high probability to precise image reconstruction
Non-local transitions enable exact solutions beyond Hamming constraints
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