Compressive Spectral Image Reconstruction using Deep Prior and Low-Rank Tensor Representation

TL;DR

This paper introduces a deep prior and low-rank tensor approach for reconstructing spectral images from compressive measurements without requiring training data, leveraging neural network structure and Tucker representation.

Contribution

It proposes a novel deep recovery framework for compressive spectral imaging that does not depend on training data, utilizing low-rank tensor modeling and neural network structure.

Findings

Effective reconstruction demonstrated through simulations and experiments.

Outperforms traditional methods relying on training data.

Utilizes Tucker tensor representation for low-dimensional structure.

Abstract

Compressive spectral imaging (CSI) has emerged as an alternative spectral image acquisition technology, which reduces the number of measurements at the cost of requiring a recovery process. In general, the reconstruction methods are based on hand-crafted priors used as regularizers in optimization algorithms or recent deep neural networks employed as an image generator to learn a non-linear mapping from the low-dimensional compressed measurements to the image space. However, these data-driven methods need many spectral images to obtain good performance. In this work, a deep recovery framework for CSI without training data is presented. The proposed method is based on the fact that the structure of some deep neural networks and an appropriated low-dimensional structure are sufficient to impose a structure of the underlying spectral image from CSI. We analyzed the low-dimension structure via the Tucker representation, modeled in the first net layer. The proposed scheme is obtained by minimizing the $\ell_2$-norm distance between the compressive measurements and the predicted measurements, and the desired recovered spectral image is formed just before the forward operator. Simulated and experimental results verify the effectiveness of the proposed method.