Enhanced 3DTV Regularization and Its Applications on Hyper-spectral Image Denoising and Compressed Sensing

Abstract

The 3-D total variation (3DTV) is a powerful regularization term, which encodes the local smoothness prior structure underlying a hyper-spectral image (HSI), for general HSI processing tasks. This term is calculated by assuming identical and independent sparsity structures on all bands of gradient maps calculated along spatial and spectral HSI modes. This, however, is always largely deviated from the real cases, where the gradient maps are generally with different while correlated sparsity structures across all their bands. Such deviation tends to hamper the performance of the related method by adopting such prior term. To this issue, this paper proposes an enhanced 3DTV (E-3DTV) regularization term beyond conventional 3DTV. Instead of imposing sparsity on gradient maps themselves, the new term calculated sparsity on the subspace bases on the gradient maps along their bands, which naturally encode the correlation and difference across these bands, and more faithfully reflect the insightful configurations of an HSI. The E-3DTV term can easily replace the previous 3DTV term and be embedded into an HSI processing model to ameliorate its performance. The superiority of the proposed methods is substantiated by extensive experiments on two typical related tasks: HSI denoising and compressed sensing, as compared with state-of-the-arts designed for both tasks.

Piecewise Weighted Smoothing Regularization in Tight Framelet Domain for Hyperspectral Image Restoration

“…In addition, the runtime (seconds) is also considered as the index to compute complexity. Especially, five state-of-the-art methods are employed as the baselines to conduct performance comparison, including deep-learningbased HySuDeep (Subspace representation and deep CNN Image prior) [15], tensor-decomposition-based LRTDGS (Weighted group sparsity-regularized low-rank tensor decomposition) [24], matrix-factorization-based E-3DTV (Enhanced 3-D total variation) [36], SNLRSF (Subspace-based nonlocal low-Rank and sparse factorization method) [33] and F-LRNMF (Framelet-regularized low-rank nonnegative matrix factorization method) [34].…”

“…In addition, total variation regularization is also an efficient method to explore the spatial-spectral local smoothness of HSI [35]. For example, Peng et al [36] firstly introduced a enhanced 3-D total variation into HSI denoising model. Although spectral and abundance signatures have respective explicit physical meaning, reshaping hyperspectral datacube into matrix form will cause certain loss of structure information [37].…”

Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration

“…We perform two kinds of compressed measurements in the encoder stage to evaluate the efficiency of the proposed NGmeet reconstruction method. First, the same as in [16], [40], we assume that the original HSI is available, and the random permuted Hadamard transform operator is adopted to compress (decoder) the image. Second, as introduced in [51], [57], a compressive sensor is used to obtain a coded compressed image with a prior designed measurement operator, which is called compressive HSI imaging.…”

“…where h is the adjoint of h [40], [51]. The optimization of ( 19) can be efficiently solved by the preconditioned conjugate gradient method [40], [51].…”