Robust hyperspectral image recovery from low-resolution quantized incomplete observations

Abstract

Quantization is fundamental to hyperspectral imaging (HSI) systems but low-bit quantization introduces strong nonlinear distortions that impede accurate recovery. Real-world HSIs also suffer from missing entries and mixed noise: dense sub-Gaussian noise from sensors and sparse outliers due to environment or hardware faults. To address these challenges, we inject random dithering – a uniform, zero-mean perturbation applied before quantization – to linearize the otherwise nonlinear quantizer in expectation. This physical insight lets us recover the original signal with a unified framework: an ${\ell }_2$ loss to suppress dense noise (leveraging the dithered quantizer's unbiasedness) and an ${\ell }_1$ penalty to remove sparse outliers. Furthermore, we introduce a Representative Coefficient Total Variation (RCTV) regularizer, which mirrors the piecewise-smooth nature of HSI spectra and spatial textures and can also capture low-rank structure via matrix factorization. RCTV not only provides a clear physical basis (contiguous spectral bands and spatial regions change gradually) but also reduces computation by focusing on representative coefficients. Empirical results on real HSI datasets demonstrate that our method substantially outperforms existing techniques in both reconstruction fidelity and runtime under low-bit quantization with missing data and mixed noise. The code of our algorithm is released at https://github.com/Yuhong163/textqrctv.