# Band-limited implicit neural representations for diffusion-weighted imaging denoising

## TL;DR

This paper introduces a new method for improving the quality of diffusion-weighted imaging by reducing noise while preserving important tissue details.

## Contribution

The novel BL-INR framework uses band-limited positional encoding to suppress noise without blurring tissue boundaries in DWI.

## Key findings

- BL-INR outperformed existing methods in visual quality across four anatomical regions in clinical data.
- Under SNR = 1, BL-INR achieved a peak SNR of 35.44 and structural similarity index of 0.933.
- Phantom experiments showed BL-INR had the smallest apparent diffusion coefficient value error among all methods.

## Abstract

Purpose. Diffusion-weighted imaging (DWI) has significant value in disease diagnosis and treatment response monitoring, but its inherent low signal-to-noise ratio (SNR) severely affects image quality and quantification accuracy. Existing denoising techniques often blur important tissue boundary information when suppressing noise. Methods. This study proposes a band-limited implicit neural representation (BL-INR) framework for DWI denoising. The method introduces BL positional encoding based on the frequency response characteristics of the sinc function to restrict INR models from learning high-frequency noise while maintaining strong signal representation capabilities. Furthermore, multi-b-value DWI and structural MRI from the same patient are integrated as anatomical priors, exploiting the correlation between true signals and the statistical independence of noise to achieve effective denoising. Main Results. In clinical DWI data evaluation across four anatomical regions (brain, head and neck, abdomen, and pelvis), BL-INR’s visualization results were superior to existing methods. Under extremely low SNR conditions (SNR = 1) in simulated noise experiments, BL-INR achieved a peak SNR of 35.44 and structural similarity index of 0.933, significantly outperforming other methods. Phantom denoising results showed that BL-INR achieved an average apparent diffusion coefficient value error of only \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{upgreek}
\usepackage{mathrsfs}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$4.57 \times 10^{-5}$\end{document}4.57×10−5 mm2 s−1, the smallest among all methods. Significance. BL-INR provides a novel approach for DWI denoising by limiting the frequency of INR input positional encoding. Its self-supervised learning characteristics require no paired training data and allow convenient clinical application. The method enables the derivation of accurate diffusion parameters, providing a reliable foundation for DWI-based quantitative analysis with significant clinical application value.