arXiv subjects

Jens Renders

Publications and source records attributed to Jens Renders.

4 recordsLinked to original sources

arXiv2026

From Block-encoding to Generalized Quantum Signal Processing: Principles, Algorithms and Applications

Modern quantum algorithms are increasingly formulated as coherent procedures for implementing polynomial transformations of operators and singular values. This perspective provides a powerful and unifying language for quantum algorithm design, connecting a wide range of distinct problems through five closely related key tools: block-encoding, qubitization, QSP, QSVT and GQSP. Block-encoding embeds non-unitary matrices into larger unitaries; qubitization converts block-encodings into structured operators; QSP, QSVT and GQSP enable polynomial transformations with near-optimal query complexity. Together, these techniques form a general toolkit for transforming matrix functions into implementable quantum circuits. This paper develops these techniques from first principles as a unified framework for constructing quantum algorithms. We apply this framework to representative applications to highlight design principles and demonstrate how distinct algorithms can be constructed from a unified sequence of operator transformations. A central contribution is a systematic decision workflow for selecting the appropriate approach according to the operator structure and the desired transformation polynomial. This perspective clarifies when direct GQSP or through qubitization, or Laurent expansion, or QSVT is most appropriate. We organize algorithmic design into an end-to-end pipeline: identifying the target matrix function, constructing an appropriate block-encoding, determining the relevant spectral domain, designing a polynomial or Laurent-polynomial approximation, synthesizing the phase factors, and translating the transformation into an executable quantum circuit. By applying this unified framework to example applications, we showcase a practical methodology for reasoning, designing, and implementing quantum algorithms based on polynomial transformations.

quant-ph↗

arXiv2025

SAMCIRT: A Simultaneous Reconstruction and Affine Motion Compensation Technique for Four Dimensional Computed Tomography (4DCT)

The majority of the recent iterative approaches in 4DCT not only rely on nested iterations, thereby increasing computational complexity and constraining potential acceleration, but also fail to provide a theoretical proof of convergence for their proposed iterative schemes. On the other hand, the latest MATLAB and Python image processing toolboxes lack the implementation of analytic adjoints of affine motion operators for 3D object volumes, which does not allow gradient methods using exact derivatives towards affine motion parameters. In this work, we propose the Simultaneous Affine Motion-Compensated Image Reconstruction Technique (SAMCIRT)- an efficient iterative reconstruction scheme that combines image reconstruction and affine motion estimation in a single update step, based on the analytic adjoints of the motion operators then exact partial derivatives with respect to both the reconstruction and the affine motion parameters. Moreover, we prove the separated Lipschitz continuity of the objective function and its associated functions, including the gradient, which supports the convergence of our proposed iterative scheme, despite the non-convexity of the objective function with respect to the affine motion parameters. Results from simulation and real experiments show that our method outperforms the state-of-the-art CT reconstruction with affine motion correction methods in computational feasibility and projection distance. In particular, this allows accurate reconstruction for a real, nonstationary diamond, showing a novel application of 4DCT.

eess.IV↗

arXiv2023

Region-based motion-compensated iterative reconstruction technique for dynamic computed tomography

Current state-of-the-art motion-based dynamic computed tomography reconstruction techniques estimate the deformation by considering motion models in the entire object volume although occasionally the proper change is local. In this article, we address this issue by introducing the region-based Motion-compensated Iterative Reconstruction Technique (rMIRT). It aims to accurately reconstruct the object being locally deformed during the scan, while identifying the deformed regions consistently with the motion models. Moreover, the motion parameters that correspond to the deformation in those areas are also estimated. In order to achieve these goals, we consider a mathematical optimization problem whose objective function depends on the reconstruction, the deformed regions and the motion parameters. The derivatives towards all of them are formulated analytically, which allows for efficient reconstruction using gradient-based optimizers. To the best of our knowledge, this is the first iterative reconstruction method in dynamic CT that exploits the analytical derivative towards the deformed regions.

math.OC↗

arXiv2023

DELTA-MRI: Direct deformation Estimation from LongiTudinally Acquired k-space data

Longitudinal MRI is an important diagnostic imaging tool for evaluating the effects of treatment and monitoring disease progression. However, MRI, and particularly longitudinal MRI, is known to be time consuming. To accelerate imaging, compressed sensing (CS) theory has been applied to exploit sparsity, both on single image as on image sequence level. State-of-the-art CS methods however, are generally focused on image reconstruction, and consider analysis (e.g., alignment, change detection) as a post-processing step. In this study, we propose DELTA-MRI, a novel framework to estimate longitudinal image changes {\it directly} from a reference image and subsequently acquired, strongly sub-sampled MRI k-space data. In contrast to state-of-the-art longitudinal CS based imaging, our method avoids the conventional multi-step process of image reconstruction of subsequent images, image alignment, and deformation vector field computation. Instead, the set of follow-up images, along with motion and deformation vector fields that describe their relation to the reference image, are estimated in one go. Experiments show that DELTA-MRI performs significantly better than the state-of-the-art in terms of the normalized reconstruction error.

eess.IV↗