第10回城西大学数理応用セミナー

日時: 2026年10月23日(金) 16:00 - 18:00

場所:城西大学紀尾井町キャンパス3号棟3F3203教室
https://www.josai.ac.jp/about/campus/kioicho/#2a3841cd
https://www.josai.ac.jp/access/kioicho/


城西大学数理応用セミナーホームページへ


懇親会：申し込みフォーム （締め切り10月16日（金））


16:00 - 16:50
Speaker: Siiri Rautio (城西大学情報数理学科)

Title：Quantum Variational Regularization for Linear Inverse Problems

Abstract：
Linear inverse problems are often ill-posed and require regularization. In this talk, I present QVaR, a framework for translating Tikhonov and sparsity-regularized linear inverse problems into quadratic unconstrained binary optimization problems and corresponding quantum Hamiltonians.

Finite-time quantum evolution produces a distribution over candidate reconstructions rather than only the minimizer. We examine whether its directional variability reflects the sensitivity and Bayesian posterior geometry of the inverse problem. Experiments using simulation and the VTT Q50 quantum processor include scalar and two-variable Tikhonov problems and Haar-wavelet deconvolution with up to 40 qubits. The results show that meaningful low-energy reconstructions can be recovered through post-selection, while small spectral gaps, circuit depth, and hardware noise remain major limitations.

17:00 - 17:50
Speaker: Gyeongha Hwang (Department of Mathematics, Yeungnam University, Korea)

Title：Exact Learning for Inverse Problems from Partial Supervision (ELIPPS)

Abstract：
Undersampled inverse problems, such as sparse-view computed tomography, reduce acquisition time and radiation exposure by collecting only a limited number of measurements. Applying learning-based reconstruction methods to these problems typically requires paired training data consisting of fully sampled measurements and ground-truth images, which are often costly or physically infeasible to acquire. Current self-supervised strategies also face limitations when the sensing configurations are restricted by hardware or dose constraints to a fixed, deterministic subset of the measurement domain.

To address this, we introduce Exact Learning for Inverse Problems from Partial Supervision (ELIPPS), an incomplete self-supervised training paradigm. ELIPPS learns globally consistent reconstructions solely from incomplete forward measurements on a fixed supervision set, entirely bypassing the need for ground-truth images or fully sampled reference data. The methodology leverages invariance properties of the signal class alongside intertwining relations of the forward map to enforce equivariance within the learned reconstruction pipeline.

Our central theoretical result demonstrates that when the data distribution is invariant under specific transformations, minimizing a masked empirical risk over an equivariant function class is strictly equivalent to minimizing the full self-supervised risk. This equivalence is mathematically exact for arbitrary equivariant hypothesis classes and remains robust under signal-dependent noise models, such as the Poisson noise inherent to low-dose tomography. Furthermore, for scenarios where the underlying frame-type coverage condition is only approximately satisfied on a discrete grid, we establish a stability estimate bounded by the associated frame constants and the irreducible error of the inverse problem.

We realize the ELIPPS framework for computed tomography by explicitly exploiting rotation and reflection invariances. Numerical experiments evaluating sparse-view reconstruction and detector upscaling demonstrate that ELIPPS substantially outperforms naive masked supervision. The framework successfully reaches the same order of accuracy as reference models trained with full, clean measurements.