Hyperspectral Imagery Compressive Sensing Using Structured Sparse Representation

Hyperspecral imaging technique has been widely exploited in various civilian and military applications,such as remote sensing,resource exploration,environment monitoring,digital agriculture and biopharmaceutics,etc.Although spectral information can benefit better detecting or identifying various objects from the cluttered scene,abundant spectral information results in the volume of hyperspectral images(HSIs)to be huge,which greatly increases the hardware resources consumption in HSI imaging,transmission and storage.Moreover,with the developing HSI applications as well as high-resolution imaging technique,the problem is worsen.Therefore,developing an effective HSI compression method to reduce the hardware resources consumption is a foundation problem in HSIs applications.Different from traditional image compression schemes,compressive sensing only collects a few compressed measurements of the original image during imaging and then reconstructs the desired image accordingly when the image is required.This enables to greatly reduce the hardware resources consumption in imaging,transmission and storage.Inspired by this,increasing attention has been paid on investigating the hyperspectral compressive sensing technique.However,most of the existing hyperspectral compressive sensing methods fail to well capture the spatial-spectral structure of the HSI,thus their reconstruction accuracy can be further improved to comply with the requirement in practical applications.To address this problem,this study mainly focuses on exploiting the structured sparse representation of HSIs according to their inherent spatial-spectral structure,and the corresponding hyperspectral compressive sensing reconstruction techniques.Extensive experiments on real HSIs demonstrate the effectiveness of the proposed methods.Specifically,this study mainly contributes in the following four aspects:(1)Considering that most of existing methods fail to depict the underlying structured sparsity in each spectra of an HSI,this study proposes a reweighted Laplace prior based hyperspectral compressive sensing reconstruction method.To capture the structured sparsity in spectra of an HSI,this method proposes a reweighed Laplace prior and imposes the prior on the representation of the latent HSI given a spectral dictionary.Then,latent variable based sparse learning method is employed to integrate the prior learning,sparse representation reconstruction and noise estimation into a unified variational framework,which can be effectively solved by an alternative minimizing scheme.Since the unified framework depicts the dependency among all unknown variables as well as the observed measurements in details,the proposed method is able to noise-robust learn the data-specific structured sparsity in an HSI.Through regularizing the reconstruction procedure with the learned structured sparsity,the reconstruction accuracy can be further improved.Extensive experimental results on HSI compressive sensing reconstruction demonstrate that the proposed method outperforms several state-of-the-art compressive sensing reconstruction methods in terms of reconstruction accuracy and robustness to noise corruption.(2)To overcome the problem resulted from exploiting the sparsity in spectra of an HSI with a fixed spectral dictionary,this study proposes a dictionary learning based hyperspectral compressive sensing reconstruction method.On the basis of the proposed reweighted Laplace prior for the sparse representation of the latent HSI,this method further proposes a structured dictionary prior on the unknown spectral dictionary,which provides a complete model for the sparse representation of an HSI.Then,inspired by the idea of alternative minimization,this method reduces the reconstruction problem into two simpler subproblems,including a sparse representation reconstruction problem and a structured dictionary learning problem.These two subproblmes are alternatively optimized in each iteration until convergence to produce the final reconstruction results.It is noticeable that each subproblem is optimized with the latent variable based learning method,which enables to model the correlation of all unknown variables as well as the observation into a unified optimization framework.By doing this,this method can noise-robust learn the image-specific spectral dictionary,with which the HSI can be completely sparsified and thus the ultimate reconstruction accuracy is improved.Experimental results demonstrate that the proposed method surpasses several state-of-the-art compressive sensing reconstruction methods in reconstruction accuracy as well as the robustness to noise corruption.In addition,with the learned spectral dictionary,an HSI can be further sparsified and the structure information in the resulted sparse representation can be easily revealed.(3)Aiming at solving the problem that the spatial structure of HSI is prone to be corrupted by the reconstruction method only depending on the spectral sparsity,this study proposes a local-filtering based hyperspectral compressive sensing reconstruction method.This method firstly reveals the nature of those methods only depending on spectral sparsity in failing to preserve the spatial structure of the HSI.Then,inspired by the obvious similarity in local region of an HSI,this method develops a novel linear filtering scheme which filters the result reconstructed by the spectral sparsity based method as a post-processing step.Different from the heuristic filtering operation,this method determines the filtering weights based on the spectral similarity in local regions.Compared with those spectral sparsity based compressive sensing reconstruction methods,the proposed method shows higher reconstruction accuracy in extensive experiments.(4)To well depict the spatial-spectral structure in an HSI as well as further improving the reconstruction accuracy,this study proposes a cluster sparsity field based hyperpsectral compressive sensing reconstruction method.In this method,a novel cluster sparsity field prior model is proposed to regularize the sparse representation of the HSI,which simultaneously captures the structured sparsity in spectra as well as the intra-cluster graph structure in spatial domain with a joint prior distribution model.In addition,several hyper-prior distribution models are developed for parameters in the prior model to enlarge the capacity of the prior model.Then,through approximating the prior model,this method employs the latent variable based learning scheme to integrate prior model learning,sparse representation reconstruction and noise estimation into a unified variational framework for optimization.On one hand,the proposed prior model is able to well depict the spatial-spectral structure of HSIs.On the other hand,the prior model parameters can be data-adaptively and noise-robust learned from the observed measurements.Both of these two aspects benefit a better image representation model,with which the reconstruction performance can be further improved.Experimental results verify the effectiveness of the proposed method in reconstruction as well as its superiority over several state-of-the-art compressive sensing reconstruction methods.