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...1024× 32) hyperspectral imageXwhich contains scene reflectance measured at 32 different frequency channels, acquired by a low-noise Peltier-cooled digital camera in the wavelength range of 400–720 nm =-=[91]-=-. Within the Kronecker-CS setting, the tensor of compressive measurements Y was obtained by multiplying the frontal slices by random Gaussian sensing matrices Φ(1) ∈ RM1×1024 and Φ(2) ∈ RM2×1024 (M1, ...

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...; V) is always positive and independent of the scale. Methods Estimates of differential entropies were based on data generated from a set of 50 hyperspectral images of natural rural and urban scenes (=-=Foster, Amano, Nascimento, & Foster, 2006-=-; Nascimento, Ferreira, & Foster, 2002). See Linhares et al. (2008) for thumbnail images. Each hyperspectral image had dimensions e1344 1024 pixels and spectral range 400–720 nm sampled at 10-nm inter...

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...sider a scene illuminated by a spatially uniform global illuminant with incident spectral radiance eðÞ at wavelength . Suppose that at a point ðx; yÞ in the scene the effective spectral reflectance =-=[15]-=- is ð;x; yÞ so that the reflected spectral radiance is given by cð;x; yÞ eðÞð;x; yÞ.1 Suppose that this reflected spectrum is sampled by the long-, medium-, and short-wavelength-sensitive (con...

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...ny given wavelength l, is characterised by its mean (m), variance (s2) and amplitude (a): G l; m,s,að Þ~ a s ffiffiffiffiffi 2p p exp { l{mð Þ 2 2s2 ! By mixing a number of Gaussians together, more complex and realistic SRFs can be defined: G l;Hð Þ~ 1 n Xn i~1 G l; mi,si,aið Þ where H is the set of model parameters defining n Gaussian components. To test the natural relevance of this model, we fitted such a mixture of Gaussians to each of a sample of pixels from hyperspectral images of natural scenes. These are rural scenes, principally vegetative, filmed under clear skies in direct sunlight [24]. We use the published estimated reflectance spectra of random portions of the scenes. Using three Gaussian components fitted using a standard least-squares optimisation procedure, this analysis resulted in r-squared scores in the range 0.91–0.96, demonstrating that natural surface reflectances are indeed accurately modelled in this way. (See Methods, ‘‘Fitting Gaussians to hyperspectral data’’ for details.) To complete our model of natural scenes, we model the illumination of the synthetic surfaces just described with natural daylight, as defined by the CIE ‘‘standard illuminant’’ D65. To cal...

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...t, UK), with sampling frequency 250 Hz, generating a sequence of horizontal and vertical coordinates at 4-ms intervals. B. Visual Stimuli Twenty natural scenes were rendered from hyperspectral images =-=[36]-=- under daylights with correlated color temperature 6500 K, corresponding to typical daylight. The test target, a gray sphere (Munsell N7), was superimposed digitally. The images on the screen subtende...

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...to simulate the CASSI measurements. The RGB images are available and aligned well with the hyperspectral images. 1) Nature scenes: We first consider the hyperspectral images of natural scenes used in =-=[48]-=-6. There are Nλ = 33 channels (400-720nm with a 10nm interval) and we resize each image to Nx = Ny = 512. The PSNR of each reconstructed spectral channel with mean values and standard deviations (acro...