Multispectral Image Restoration by Generalized Opponent Transformation Total Variation

TL;DR

This work introduces Generalized Opponent Transformation Total Variation (GOTTV) to address multispectral image restoration by transferring the TV regularization to a generalized opponent domain. The authors define a $d\times d$ orthogonal transformation with a final averaging row to produce two components: an opponent-structured gradient term and an averaging-structured term, enabling effective denoising and edge preservation for MSI. They formulate a MAP-based restoration model using GOTTV, establish convexity and existence/uniqueness under standard operators, and solve the resulting problem via an ADMM scheme with FFT-based subproblems. Numerical experiments on denoising and deblurring tasks demonstrate superior MPSNR and MSSIM performance and improved texture preservation compared to state-of-the-art MSI-TV methods, with robustness to the choice of opponent transform. The approach offers a principled way to exploit spectral correlations in MSI and yields practically impactful improvements for spectral-spatial image restoration.

Abstract

Multispectral images (MSI) contain light information in different wavelengths of objects, which convey spectral-spatial information and help improve the performance of various image processing tasks. Numerous techniques have been created to extend the application of total variation regularization in restoring multispectral images, for example, based on channel coupling and adaptive total variation regularization. The primary contribution of this paper is to propose and develop a new multispectral total variation regularization in a generalized opponent transformation domain instead of the original multispectral image domain. Here opponent transformations for multispectral images are generalized from a well-known opponent transformation for color images. We will explore the properties of generalized opponent transformation total variation (GOTTV) regularization and the corresponding optimization formula for multispectral image restoration. To evaluate the effectiveness of the new GOTTV method, we provide numerical examples that showcase its superior performance compared to existing multispectral image total variation methods, using criteria such as MPSNR and MSSIM.

Figures (25)

• Figure 1: Pseudo-color images (R-26, G-20, B-4) of objects for comparison.
• Figure 2: Channel-wise Frobenius norm information for cloth and face.
• Figure 3: Partial view of cloth in different channels.
• Figure 4: Spectrum-by-spectrum PSNR comparison chart of different methods for cloth.
• Figure 5: Spectrum-by-spectrum SSIM comparison chart of different methods for cloth.

Theorems & Definitions (10)

• Theorem 3.1
• Proof 1
• Theorem 3.2
• Proof 2
• Theorem 3.3
• Proof 3
• Theorem 3.4
• Proof 4
• Theorem 3.5
• Proof 5