Hyperspectral Image Recovery via Hybrid Regularization

TL;DR

This paper introduces a novel hybrid regularization approach for hyperspectral image recovery, combining spatial total variation and spectral sparsity, solved efficiently with an accelerated proximal method, demonstrating superior performance on real data.

Contribution

The paper proposes a new composite regularization model for hyperspectral image recovery and an efficient accelerated proximal-subgradient algorithm with proven convergence.

Findings

Achieves high-quality hyperspectral image recovery from limited measurements.

Outperforms classical basis-pursuit denoising algorithms in experiments.

Requires only a small fraction of data size for effective reconstruction.

Abstract

Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy measurements. To perform the recovery while taking full advantage of the prior knowledge, we formulate a composite cost function containing a square-error data-fitting term and two distinct regularization terms pertaining to spatial and spectral domains. The regularization for the spatial domain is the sum of total-variation of the image frames corresponding to all spectral bands. The regularization for the spectral domain is the l1-norm of the coefficient matrix obtained by applying a suitable sparsifying transform to the spectra of the pixels. We use an accelerated proximal-subgradient method to minimize the formulated cost function. We analyze the performance of the proposed algorithm and prove its convergence. Numerical simulations using real hyperspectral images exhibit that the proposed algorithm offers an excellent recovery performance with a number of measurements that is only a small fraction of the hyperspectral image data size. Simulation results also show that the proposed algorithm significantly outperforms an accelerated proximal-gradient algorithm that solves the classical basis-pursuit denoising problem to recover the hyperspectral image.