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A new multiplicative denoising variational model based on mth root transformation.

Sangwoon Yun¹, Hyenkyun Woo

¹Department of Mathematics Education, Sung Kyun Kwan University, Seoul, Korea. sangwoony@gmail.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 31, 2012

Summary

This study introduces an m-th root function to improve multiplicative noise removal in synthetic aperture radar (SAR) images. The new method offers better performance and efficiency than existing log-transformed models.

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Area of Science:

Image processing
Signal processing
Remote sensing

Background:

Coherent imaging systems like synthetic aperture radar (SAR) suffer from multiplicative noise.
Variational models with total variation (TV) regularization are effective for noise reduction but often face non-convexity issues.
Existing methods use logarithmic transformation to achieve convexity, which can be computationally challenging.

Purpose of the Study:

To develop a novel variational model for multiplicative noise removal in SAR images.
To address the non-convexity problem in fidelity terms without using logarithmic transformation.
To propose an efficient and parallelizable algorithm for noise reduction in large-scale SAR data.

Main Methods:

Exploited an m-th root function to relax the non-convexity of the variational model.
Adapted a linearized proximal alternating minimization algorithm to solve the proposed model efficiently.
Avoided inner iterations for subproblem solving, enhancing computational efficiency.

Main Results:

The proposed m-th root transformed model demonstrates superior performance in multiplicative noise removal compared to the log-transformed convex model.
The adapted algorithm is simple, highly parallelizable, and efficient for processing large SAR images.
The method effectively preserves image edges while reducing multiplicative noise.

Conclusions:

The m-th root function offers a viable alternative to logarithmic transformation for addressing non-convexity in variational models for SAR image noise reduction.
The linearized proximal alternating minimization algorithm provides an efficient and practical solution for the proposed model.
This approach significantly improves the quality of SAR images affected by multiplicative noise.