Relative intensity Wavelength (nm) KRISM Spectrometer spatial code measured spectrum S-polarized light polarizing beam splitter LCoS SLM diffraction grating P-polarization S-polarization operator #1. spatially-coded spectrum measurement spectral code measured spatial image P-polarized light operator #2. spectrally-coded spatial measurement 1 1 Fig. 1.Hyperspectral imagers resolve scenes at high spatial and spectral resolutions. We propose a novel architecture called KRISM that provides the ability to implement two operators: a spatially-coded spectrometer and a spectrally-coded spatial imager. By iterating between the two, we can acquire a low rank approximation of the hyperspectral image in a light efficient manner with very few measurements. The left image shows optical schematics for implementing the two operators. On the right, we show a hyperspectral image of a scene illuminated with a compact fluorescent lamp (CFL) acquired using our lab prototype. The proposed method enables high spatial and spectral resolution as observed in the zoomed-in image patches and CFL peaks, respectively.We present an adaptive imaging technique that optically computes a lowrank approximation of a scene's hyperspectral image, conceptualized as a matrix. Central to the proposed technique is the optical implementation of two measurement operators: a spectrally-coded imager and a spatially-coded spectrometer. By iterating between the two operators, we show that the top singular vectors and singular values of a hyperspectral image can be adaptively and optically computed with only a few iterations. We present an optical design that uses pupil plane coding for implementing the two operations and show several compelling results using a lab prototype to demonstrate the effectiveness of the proposed hyperspectral imager.
DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of two vectors), where each low-rank tensor is generated by a deep network (DN) that is trained in a self-supervised manner to minimize the mean-square approximation error. Our key observation is that the implicit regularization inherent in DNs enables them to capture nonlinear signal structures (e.g., manifolds) that are out of the reach of classical linear methods like the singular value decomposition (SVD) and principal components analysis (PCA). Furthermore, in contrast to the SVD and PCA, whose performance deteriorates when the tensor's entries deviate from additive white Gaussian noise, we demonstrate that the performance of DeepTensor is robust to a wide range of distributions. We validate that DeepTensor is a robust and computationally efficient drop-in replacement for the SVD, PCA, nonnegative matrix factorization (NMF), and similar decompositions by exploring a range of real-world applications, including hyperspectral image denoising, 3D MRI tomography, and image classification. In particular, DeepTensor offers a 6dB signal-to-noise ratio improvement over standard denoising methods for signal corrupted by Poisson noise and learns to decompose 3D tensors 60 times faster than a single DN equipped with 3D convolutions.
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