Monika Pandey | Searcharxiv

arXiv2025

The Complex-Step Integral Transform

Building on the well-established connection between the Hilbert transform and derivative operators, and motivated by recent developments in complex-step differentiation, we introduce the Complex-Step Integral Transform (CSIT): a generalized integral transform that combines analytic continuation, derivative approximation, and multi-scale smoothing within a unified framework. A spectral analysis shows that the CSIT preserves phase while suppressing high-wavenumber noise, offering advantages over conventional Fourier derivatives. We discuss the roles of the real and imaginary step parameters, compare FFT-based and interpolation-based implementations, and demonstrate the method on the advection equation and instantaneous-frequency computation. Results show that the CSIT yields smoother, more robust attributes than Hilbert-based methods and provides built-in stabilization for PDE solvers. The CSIT thus represents a flexible alternative for numerical differentiation, spectral analysis, and seismic signal processing. The method opens several avenues for future work, including non-periodic implementations, adaptive parameter selection, and integration with local interpolation frameworks such as high-order Finite-Element methods.

math.NA↗

arXiv2025

Predicting Anthropometric Body Composition Variables Using 3D Optical Imaging and Machine Learning

Accurate prediction of anthropometric body composition variables, such as Appendicular Lean Mass (ALM), Body Fat Percentage (BFP), and Bone Mineral Density (BMD), is essential for early diagnosis of several chronic diseases. Currently, researchers rely on Dual-Energy X-ray Absorptiometry (DXA) scans to measure these metrics; however, DXA scans are costly and time-consuming. This work proposes an alternative to DXA scans by applying statistical and machine learning models on biomarkers (height, volume, left calf circumference, etc) obtained from 3D optical images. The dataset consists of 847 patients and was sourced from Pennington Biomedical Research Center. Extracting patients' data in healthcare faces many technical challenges and legal restrictions. However, most supervised machine learning algorithms are inherently data-intensive, requiring a large amount of training data. To overcome these limitations, we implemented a semi-supervised model, the $p$-Laplacian regression model. This paper is the first to demonstrate the application of a $p$-Laplacian model for regression. Our $p$-Laplacian model yielded errors of $\sim13\%$ for ALM, $\sim10\%$ for BMD, and $\sim20\%$ for BFP when the training data accounted for 10 percent of all data. Among the supervised algorithms we implemented, Support Vector Regression (SVR) performed the best for ALM and BMD, yielding errors of $\sim 8\%$ for both, while Least Squares SVR performed the best for BFP with $\sim 11\%$ error when trained on 80 percent of the data. Our findings position the $p$-Laplacian model as a promising tool for healthcare applications, particularly in a data-constrained environment.

cs.LG↗