Divergence Phase Index: A Riesz-Transform Framework for Multidimensional Phase Difference Analysis

• URL: http://arxiv.org/abs/2510.04426v1
• Date: Mon, 06 Oct 2025 01:39:09 GMT
• Title: Divergence Phase Index: A Riesz-Transform Framework for Multidimensional Phase Difference Analysis
• Abstract summary: We introduce the Divergence Phase Index (DPI), a novel framework for quantifying phase differences in one and multidimensional signals.<n>Based on classical Hilbert Transform phase measures, the DPI extends these principles to higher dimensions, offering a geometry-aware metric.<n>We applied this method on both synthetic and real-world datasets, including intracranial EEG (iEEG) recordings during epileptic seizures.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the Divergence Phase Index (DPI), a novel framework for quantifying phase differences in one and multidimensional signals, grounded in harmonic analysis via the Riesz transform. Based on classical Hilbert Transform phase measures, the DPI extends these principles to higher dimensions, offering a geometry-aware metric that is invariant to intensity scaling and sensitive to structural changes. We applied this method on both synthetic and real-world datasets, including intracranial EEG (iEEG) recordings during epileptic seizures, high-resolution microscopy images, and paintings. In the 1D case, the DPI robustly detects hypersynchronization associated with generalized epilepsy, while in 2D, it reveals subtle, imperceptible changes in images and artworks. Additionally, it can detect rotational variations in highly isotropic microscopy images. The DPI's robustness to amplitude variations and its adaptability across domains enable its use in diverse applications from nonlinear dynamics, complex systems analysis, to multidimensional signal processing.

Related papers

• Radiation, Rotation and Scale Invariant Feature Descriptor for Multimodal Image Matching [17.63368151646172]
  We propose a radiation, rotation, and scale invariant (RRSI) feature descriptor for multimodal image matching.<n>RRSI supports the full rotation range from 0 to 360 degrees and scale factors up to four.<n>Its ability is validated on multimodal images from computer vision, remote sensing, and medical imaging.
  arXiv  Detail & Related papers  (2026-09-06T02:32:03Z)
• Universal Pansharpening Foundation Model [67.10467574892282]
  Pansharpening generates the high-resolution multi-spectral (MS) image by integrating spatial details from a texture-rich panchromatic (PAN) image and spectral attributes from a low-resolution MS image.<n>We present FoundPS, a universal pansharpening foundation model for satellite-agnostic and scene-robust fusion.
  arXiv  Detail & Related papers  (2026-03-04T08:30:15Z)
• Differential privacy representation geometry for medical image analysis [1.828619151598757]
  Differential privacy (DP)'s effect in medical imaging is typically evaluated only through end-to-end performance.<n>We introduce Differential Privacy Representation Geometry for Medical Imaging (DP-RGMI), a framework that interprets DP as a structured transformation of representation space.<n>We show that DP is consistently associated with a utilization gap even when linear separability is largely preserved.
  arXiv  Detail & Related papers  (2026-03-01T13:30:36Z)
• GDROS: A Geometry-Guided Dense Registration Framework for Optical-SAR Images under Large Geometric Transformations [24.22541638346487]
  We propose GDROS, a geometry-guided dense registration framework leveraging global cross-modal image interactions.<n>First, we extract cross-modal deep features from optical and SAR images through a CNN-Transformer hybrid feature extraction module.<n>We then implement a least squares regression (LSR) module to geometrically constrain the predicted dense optical flow field.
  arXiv  Detail & Related papers  (2025-11-01T15:40:34Z)
• Accelerating 3D Photoacoustic Computed Tomography with End-to-End Physics-Aware Neural Operators [74.65171736966131]
  Photoacoustic computed tomography (PACT) combines optical contrast with ultrasonic resolution, achieving deep-tissue imaging beyond the optical diffusion limit.<n>Current implementations require dense transducer arrays and prolonged acquisition times, limiting clinical translation.<n>We introduce Pano, an end-to-end physics-aware model that directly learns the inverse acoustic mapping from sensor measurements to volumetric reconstructions.
  arXiv  Detail & Related papers  (2025-09-11T23:12:55Z)
• DiffusionSfM: Predicting Structure and Motion via Ray Origin and Endpoint Diffusion [53.70278210626701]
  We propose a data-driven multi-view reasoning approach that directly infers 3D scene geometry and camera poses from multi-view images.<n>Our framework, DiffusionSfM, parameterizes scene geometry and cameras as pixel-wise ray origins and endpoints in a global frame.<n>We empirically validate DiffusionSfM on both synthetic and real datasets, demonstrating that it outperforms classical and learning-based approaches.
  arXiv  Detail & Related papers  (2025-05-08T17:59:47Z)
• Fourier-Based 3D Multistage Transformer for Aberration Correction in Multicellular Specimens [1.288373532663608]
  We introduce AOViFT -- a machine learning-based aberration sensing framework built around a 3D multistage Vision Transformer.<n> AOViFT infers aberrations and restores diffraction-limited performance in puncta-labeled specimens.<n>We validated AOViFT on live gene-edited zebrafish embryos, demonstrating its ability to correct spatially varying aberrations.
  arXiv  Detail & Related papers  (2025-03-16T17:59:20Z)
• Polyhedra Encoding Transformers: Enhancing Diffusion MRI Analysis Beyond Voxel and Volumetric Embedding [9.606654786275902]
  In this paper, we propose a novel method called Polyhedra Transformer (PE-Transformer) for dMRI, designed specifically to handle spherical signals.<n>Our approach involves projecting an icosahedral unit sphere to resample signals from predetermined directions. These resampled signals are then transformed into embeddings, which are processed by a transformer encoder that incorporates orientational information reflective of the icosahedral structure.
  arXiv  Detail & Related papers  (2025-01-23T03:32:52Z)
• On Sensitivity and Robustness of Normalization Schemes to Input Distribution Shifts in Automatic MR Image Diagnosis [58.634791552376235]
  Deep Learning (DL) models have achieved state-of-the-art performance in diagnosing multiple diseases using reconstructed images as input. DL models are sensitive to varying artifacts as it leads to changes in the input data distribution between the training and testing phases. We propose to use other normalization techniques, such as Group Normalization and Layer Normalization, to inject robustness into model performance against varying image artifacts.
  arXiv  Detail & Related papers  (2023-06-23T03:09:03Z)
• Exploring Invariant Representation for Visible-Infrared Person Re-Identification [77.06940947765406]
  Cross-spectral person re-identification, which aims to associate identities to pedestrians across different spectra, faces a main challenge of the modality discrepancy. In this paper, we address the problem from both image-level and feature-level in an end-to-end hybrid learning framework named robust feature mining network (RFM) Experiment results on two standard cross-spectral person re-identification datasets, RegDB and SYSU-MM01, have demonstrated state-of-the-art performance.
  arXiv  Detail & Related papers  (2023-02-02T05:24:50Z)
• Negligible effect of brain MRI data preprocessing for tumor segmentation [36.89606202543839]
  We conduct experiments on three publicly available datasets and evaluate the effect of different preprocessing steps in deep neural networks. Our results demonstrate that most popular standardization steps add no value to the network performance. We suggest that image intensity normalization approaches do not contribute to model accuracy because of the reduction of signal variance with image standardization.
  arXiv  Detail & Related papers  (2022-04-11T17:29:36Z)
• Finding simplicity: unsupervised discovery of features, patterns, and order parameters via shift-invariant variational autoencoders [0.0]
  We develop shift-invariant variational autoencoders (shift-VAE) that allow disentangling characteristic repeating features in the images. We show that shift-VAEs balance the uncertainty in the position of the object of interest with the uncertainty in shape reconstruction.
  arXiv  Detail & Related papers  (2021-06-23T15:39:07Z)
• Leveraging Spatial and Photometric Context for Calibrated Non-Lambertian Photometric Stereo [61.6260594326246]
  We introduce an efficient fully-convolutional architecture that can leverage both spatial and photometric context simultaneously. Using separable 4D convolutions and 2D heat-maps reduces the size and makes more efficient.
  arXiv  Detail & Related papers  (2021-03-22T18:06:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.