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

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.