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A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution

Alexandros Gkillas, Dimitris Ampeliotis, Kostas Berberidis

TL;DR

This work tackles hyperspectral image deconvolution by integrating handcrafted regularizers with learnable priors in a hybrid optimization framework. It introduces DeepMix, an interpretable deep unrolling model built around a data-consistency module, a smooth-gradient prior, and a context-aware denoiser with skip connections, all trained end-to-end via a fixed-point formulation. The approach provides convergence guarantees, reduced denoiser complexity, and strong empirical performance on simulated and real-world datasets, including scenarios with unknown blur kernels. The findings highlight the value of balancing domain knowledge with learned priors to enhance restoration quality and computational efficiency in high-dimensional HSI problems.

Abstract

In recent literature there are plenty of works that combine handcrafted and learnable regularizers to solve inverse imaging problems. While this hybrid approach has demonstrated promising results, the motivation for combining handcrafted and learnable regularizers remains largely underexplored. This work aims to justify this combination, by demonstrating that the incorporation of proper handcrafted regularizers alongside learnable regularizers not only reduces the complexity of the learnable prior, but also the performance is notably enhanced. To analyze the impact of this synergy, we introduce the notion of residual structure, to refer to the structure of the solution that cannot be modeled by the handcrafted regularizers per se. Motivated by these, we propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix. Based on the proposed optimization framework, an interpretable model is developed using the deep unrolling strategy, which consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module. Recognizing the collaborative nature of these modules, this work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules. This is facilitated through the incorporation of a proper skip connection, ensuring that essential details and structures identified by other modules are effectively retained and not lost during denoising. Extensive experimental results across simulated and real-world datasets demonstrate that DeepMix is notable for surpassing existing methodologies, offering marked improvements in both image quality and computational efficiency.

A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution

TL;DR

This work tackles hyperspectral image deconvolution by integrating handcrafted regularizers with learnable priors in a hybrid optimization framework. It introduces DeepMix, an interpretable deep unrolling model built around a data-consistency module, a smooth-gradient prior, and a context-aware denoiser with skip connections, all trained end-to-end via a fixed-point formulation. The approach provides convergence guarantees, reduced denoiser complexity, and strong empirical performance on simulated and real-world datasets, including scenarios with unknown blur kernels. The findings highlight the value of balancing domain knowledge with learned priors to enhance restoration quality and computational efficiency in high-dimensional HSI problems.

Abstract

In recent literature there are plenty of works that combine handcrafted and learnable regularizers to solve inverse imaging problems. While this hybrid approach has demonstrated promising results, the motivation for combining handcrafted and learnable regularizers remains largely underexplored. This work aims to justify this combination, by demonstrating that the incorporation of proper handcrafted regularizers alongside learnable regularizers not only reduces the complexity of the learnable prior, but also the performance is notably enhanced. To analyze the impact of this synergy, we introduce the notion of residual structure, to refer to the structure of the solution that cannot be modeled by the handcrafted regularizers per se. Motivated by these, we propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix. Based on the proposed optimization framework, an interpretable model is developed using the deep unrolling strategy, which consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module. Recognizing the collaborative nature of these modules, this work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules. This is facilitated through the incorporation of a proper skip connection, ensuring that essential details and structures identified by other modules are effectively retained and not lost during denoising. Extensive experimental results across simulated and real-world datasets demonstrate that DeepMix is notable for surpassing existing methodologies, offering marked improvements in both image quality and computational efficiency.
Paper Structure (34 sections, 1 theorem, 33 equations, 3 figures, 6 tables)

This paper contains 34 sections, 1 theorem, 33 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Hyperspectral Deconvolution
  4. Deep unrolling
  5. Problem Formulation
  6. Proposed Optimization based Model
  7. Iterative Optimization algorithm
  8. Consequent Modules
  9. Data Consistency Module - Sub-problem (\ref{['eq:updateX']})
  10. Smooth Gradients Prior module - Sub-problems (\ref{['eq:updateV1']}, \ref{['eq:updateV2']}, \ref{['eq:updateV3']} )
  11. Context aware denoising module - Sub-problem (\ref{['eq:updateZ']})
  12. Overall Iterative Algorithm
  13. Proposed Interpretable Deep Unrolling model
  14. Implementation Details
  15. Fixed point Calculation: Forward and Backward pass
  16. ...and 19 more sections

Key Result

Theorem 1

Let $f_\theta(\cdot)$ be a neural network denoiser that is $\epsilon_1$-Lipschitz continuous, the conv. layers $P_1, P_2, P_3$ be $\epsilon_2, \epsilon_3, \epsilon_4$-Lipschitz continuous and let $L = \lambda_{\mathcal{H}^T\mathcal{H}, min}$ be the minimum eigenvalue of $\mathcal{H}^T\mathcal{H}$. for all $x_1, x_2 \in \mathbb{R}^d$. The iteration map is contractive if $\frac{(b_1 \epsilon_1 + b

Figures (3)

  • Figure 1: Visual results for the best performing methods in the blurring scenario (a) on the CAVE dataset. The first and second rows present the results for two different blurred images. The false color images were generated for clear visualization with the 22th, 14th and 7th channels used for red, green and blue.
  • Figure 2: Visual results for the best performing methods in the blurring scenario (b) on the Chikushei dataset. The false color images were generated for clear visualization with the 122th, 84th and 57th used for red, green and blue, respectively.
  • Figure 3: Blurred images, reference images and visual results for the best performing methods on the real-world dataset. The false color images were generated for clear visualization with the 38th, 24th and 10th channels used for red, green and blue, respectively.

Theorems & Definitions (2)

  • Theorem 1
  • proof