Multiscale image denoising using goodness-of-fit test based on EDF statistics

Area of Science:

• Digital Image Processing
• Signal Processing
• Statistical Signal Analysis

Background:

• Image noise significantly degrades visual quality and hinders subsequent analysis.
• Traditional denoising methods often struggle to preserve image details while effectively removing noise.
• Wavelet transforms are widely used for image denoising due to their ability to represent signals at different scales and orientations.

Purpose of the Study:

• To introduce two novel image denoising algorithms.
• To leverage goodness of fit (GoF) tests for robust noise identification.
• To enhance image quality by accurately separating signal from noise.

Main Methods:

• Applying GoF tests locally on wavelet coefficients obtained from Discrete Wavelet Transform (DWT) and Dual Tree Complex Wavelet Transform (DT-CWT).
• Formulating image denoising as a binary hypothesis testing problem.
• Utilizing the empirical distribution function (EDF) for GoF testing to decide between noise and signal presence.

Main Results:

• The proposed algorithms demonstrate effective noise removal at multiple image scales.
• Local GoF testing on wavelet coefficients allows for precise identification of noisy regions.
• Validation against state-of-the-art methods indicates competitive or superior denoising performance.

Conclusions:

• The novel GoF-based algorithms offer a promising approach to image denoising.
• Employing hypothesis testing with EDF-based GoF tests provides a robust framework for noise-signal discrimination.
• These methods contribute to advancing the field of digital image processing and restoration.