In this paper, we investigate a low-complexity scheme for decoding compressed hyperspectral image data. We have exploited the simplicity of the subgradient method by modifying a total variation-based regularization problem to include a residual constraint, employing convex optimality conditions to provide equivalency between the original and reformed problem statements. A scheme that utilizes spectral smoothness by calculating informed starting points to improve the rate of convergence is introduced. We conduct numerical experiments, using both synthetic and real hyperspectral data, to demonstrate the effectiveness of the reconstruction algorithm and the validity of our method for exploiting spectral smoothness. Evidence from these experiments suggests that the proposed methods have the potential to improve the quality and run times of the future compressed hyperspectral image reconstructions.

We present an algorithm that exploits the assumption that materials mix linearly in a scene to reconstruct hyperspectral images from compressed hyperspectral imaging data. With endmember spectra known a priori, we propose a simple first-order variant of the projected subgradient method that promotes low spatial variation of each material's abundance map. Combining the large decrease in computational complexity offered by assuming linear mixing with making search directions conjugate with all previous steps, and taking advantage of the characteristics of large and small steps sizes, we improve run-times by between 3 and 34 times when compared to a similar algorithm that does not assume material mixing. Additionally, the extra information provided by the material spectra typically grants improved reconstruction fidelities, particularly when the original measurements are corrupted by noise.

A novel method for blind spectral unmixing directly from compressive measurements of highly mixed hyperspectral data is presented. Unlike existing unmixing algorithms in compressed sensing (CS), our method does not assume the dominant presence of pure pixels in the underlying data. Our approach brings together multiple important priors in the hyperspectral data by penalizing the TV norm of the abundances, the variance of the endmembers as well as the geometric distances between them. The solution therefore simultaneously accounts for the internal characteristics within each material constituting the underlying data, and the external geometry between the materials under the linear mixing model. Experimental results over noisy CS measurements with highly mixed data demonstrate the effectiveness of our approach over existing methods.

A popular algorithm for unmixing hyperspectral data, namely, Winter's N-FINDR algorithm, is frequently used to benchmark other algorithms or as the basis for new algorithms. The interpretations of this algorithm within the literature are not consistent, and some of these differences have significant impact on the convergence of the algorithm. Despite this, the differences in implementation have not been explicitly acknowledged within the literature, which means that many studies are now ambiguous or incomparable. An examination of various implementations of the N-FINDR algorithm highlights that not all interpretations possess the properties asserted by Winter and that interpretations that consider each pixel multiple times generate much larger simplexes. Regardless of which implementation researchers choose to use, if they are explicit in their choice, this would allow for unambiguous comparisons.

Linear unmixing is a blind source separation problem that decomposes a hyperspectral image into the spectra of the material constituents of the scene and the abundance maps of those materials across that scene. A novel method for determining the material spectra from within the scene, AGES, is proposed based on the positional information contained within abundances generated by additivity-constrained inversion. This new approach is compared on both simulated and real data sets to the well established N-FINDR algorithm, comparing favorably in terms of computational complexity with the existing algorithm without significantly sacrificing accuracy. In addition, the algorithm has some desirable properties inherent in such an approach.

This paper describes a technique for the blind deconvolution of extended objects such as the Hubble Space Telescope (HST), scanning electron and 3D fluorescence microscope images. The blind deconvolution mechanism is based on the Richardson-Lucy (1972, 1974) algorithm and alternates between deconvolution of the image and point spread function (PSF). This form of iterative blind deconvolution differs from that typically employed in that multiple PSF iterations are performed after each image iteration. The initial estimate for the PSF is the autocorrelation of the blurred image and the edges of the image are windowed to minimise wrap around artifacts. Acceleration techniques are employed to speed restoration and results from real HST, electron microscope and 3D fluorescence images are presented.