Publications

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We present a deep learning image reconstruction method called AirNet-SNL for sparse view computed tomography. It combines iterative reconstruction and convolutional neural networks with end-to-end training. Our model reduces streak artifacts from filtered back-projection with limited data, and it trains on randomly generated shapes. This work shows promise to generalize learning image reconstruction.

Over the last 15 years, compressive sensing techniques have been developed which have the potential to greatly reduce the amount of data collected by systems while preserving the amount of information obtained. A cost of this efficiency is that a computationally-intensive optimization routine must be used to put the sensed data into a form that a person can interpret. At the same time, machine learning techniques have experienced tremendous growth as well. Machines have demonstrated the ability learn how to effectively perform tasks such as detection and classification at speeds much faster than humanly possible. Our goal in this project was to study the feasibility of using compressive sensing systems "at the edge." That is, how can compressive sensing sensors be deployed such that information is created at the remote sensor rather than sending raw data to a central processing location? Studies were performed to analyze whether machine learning could be done on the compressively sensed data in its raw form. If a machine is performing the task, is it possible to do so without putting the data into a human interpretable form? We show that this is possible for some systems, in particular a compressive sensing snapshot imaging spectrometer. Machine learning tasks were demonstrated to be more effective and more robust to noise when the machine learning algorithm worked on data in its raw form. This system is shown to outperform a traditional spectrometer. Techniques for reducing the complexity of the reconstruction routine were also analyzed. Techniques for such as data regularization, deep neural networks, and matrix completion were studied and shown to have benefits over traditional reconstruction techniques. In this project we showed that compressive sensing sensors are indeed feasible at the edge. As always, sensors and algorithms must be carefully tuned to work in the constrained environment. In this project we developed tools and techniques to enable those analyses.

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We propose a technique for reconstruction from incomplete compressive measurements. Our approach combines compressive sensing and matrix completion using the consensus equilibrium framework. Consensus equilibrium breaks the reconstruction problem into subproblems to solve for the high-dimensional tensor. This framework allows us to apply two constraints on the statistical inversion problem. First, matrix completion enforces a low rank constraint on the compressed data. Second, the compressed tensor should be consistent with the uncompressed tensor when it is projected onto the low-dimensional subspace. We validate our method on the Indian Pines hyperspectral dataset with varying amounts of missing data. This work opens up new possibilities for data reduction, compression, and reconstruction.

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We investigate deep neural networks to reconstruct and classify hyperspectral images from compressive sensing measurements. Hyperspectral sensors provide detailed spectral information to differentiate materials. However, traditional imagers require scanning to acquire spatial and spectral information, which increases collection time. Compressive sensing is a technique to encode signals into fewer measurements. It can speed acquisition time, but the reconstruction can be computationally intensive. First we describe multilayer perceptrons to reconstruct compressive hyperspectral images. Then we compare two different inputs to machine learning classifiers: compressive sensing measurements and the reconstructed hyperspectral image. The classifiers include support vector machines, K nearest neighbors, and three neural networks (3D convolutional neural networks and recurrent neural networks). The results show that deep neural networks can speed up the time for the acquisition, reconstruction, and classification of compressive hyperspectral images.

We investigate deep neural networks to reconstruct and classify hyperspectral images from compressive sensing measurements. Hyperspectral sensors provide detailed spectral information to differentiate materials. However, traditional imagers require scanning to acquire spatial and spectral information, which increases collection time. Compressive sensing is a technique to encode signals into fewer measurements. It can speed acquisition time, but the reconstruction can be computationally intensive. First we describe multilayer perceptrons to reconstruct compressive hyperspectral images. Then we compare two different inputs to machine learning classifiers: compressive sensing measurements and the reconstructed hyperspectral image. The classifiers include support vector machines, K nearest neighbors, and three neural networks (3D convolutional neural networks and recurrent neural networks). The results show that deep neural networks can speed up the time for the acquisition, reconstruction, and classification of compressive hyperspectral images.

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Compressive sensing shows promise for sensors that collect fewer samples than required by traditional Shannon-Nyquist sampling theory. Recent sensor designs for hyperspectral imaging encode light using spectral modulators such as spatial light modulators, liquid crystal phase retarders, and Fabry-Perot resonators. The hyperspectral imager consists of a filter array followed by a detector array. It encodes spectra with less measurements than the number of bands in the signal, making reconstruction an underdetermined problem. We propose a reconstruction algorithm for hyperspectral images encoded through spectral modulators. Our approach constrains pixels to be similar to their neighbors in space and wavelength, as natural images tend to vary smoothly, and it increases robustness to noise. It combines L1 minimization in the wavelet domain to enforce sparsity and total variation in the image domain for smoothness. The alternating direction method of multipliers (ADMM) simplifies the optimization procedure. Our algorithm constrains encoded, compressed hyperspectral images to be smooth in their reconstruction, and we present simulation results to illustrate our technique. This work improves the reconstruction of hyperspectral images from encoded, multiplexed, and sparse measurements.

Compressive sensing shows promise for sensors that collect fewer samples than required by traditional Shannon-Nyquist sampling theory. Recent sensor designs for hyperspectral imaging encode light using spectral modulators such as spatial light modulators, liquid crystal phase retarders, and Fabry-Perot resonators. The hyperspectral imager consists of a filter array followed by a detector array. It encodes spectra with less measurements than the number of bands in the signal, making reconstruction an underdetermined problem. We propose a reconstruction algorithm for hyperspectral images encoded through spectral modulators. Our approach constrains pixels to be similar to their neighbors in space and wavelength, as natural images tend to vary smoothly, and it increases robustness to noise. It combines L1 minimization in the wavelet domain to enforce sparsity and total variation in the image domain for smoothness. The alternating direction method of multipliers (ADMM) simplifies the optimization procedure. Our algorithm constrains encoded, compressed hyperspectral images to be smooth in their reconstruction, and we present simulation results to illustrate our technique. This work improves the reconstruction of hyperspectral images from encoded, multiplexed, and sparse measurements.

Channeled spectropolarimetry measures the spectrally resolved Stokes parameters. A key aspect of this technique is to accurately reconstruct the Stokes parameters from a modulated measurement of the channeled spectropolarimeter. The state-of-the-art reconstruction algorithm uses the Fourier transform to extract the Stokes parameters from channels in the Fourier domain. While this approach is straightforward, it can be sensitive to noise and channel cross-talk, and it imposes bandwidth limitations that cut o high frequency details. To overcome these drawbacks, we present a reconstruction method called compressed channeled spectropolarimetry. In our proposed framework, reconstruction in channeled spectropolarimetry is an underdetermined problem, where we take N measurements and solve for 3N unknown Stokes parameters. We formulate an optimization problem by creating a mathematical model of the channeled spectropolarimeter with inspiration from compressed sensing. We show that our approach o ers greater noise robustness and reconstruction accuracy compared with the Fourier transform technique in simulations and experimental measurements. By demonstrating more accurate reconstructions, we push performance to the native resolution of the sensor, allowing more information to be recovered from a single measurement of a channeled spectropolarimeter.

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Channeled linear imaging polarimeters measure the two-dimensional distribution of the linear Stokes parameters. A key aspect of this technique is to accurately reconstruct the Stokes parameters from a snapshot, modulated measurement of the channeled linear imaging polarimeter. The state-of-The-Art reconstruction takes the Fourier transform of the measurement to separate the Stokes parameters into channels. While straightforward, this approach is sensitive to channel cross-Talk and imposes bandwidth limitations that cut off high frequency details. To overcome these drawbacks, we present a reconstruction method called compressed channeled linear imaging polarimetry. In this framework, reconstruction in channeled linear imaging polarimetry is an underdetermined problem, where we measure N pixels and recover 3N Stokes parameters. We formulate an optimization problem by creating a mathematical model of the channeled linear imaging polarimeter with inspiration from compressed sensing. Through simulations, we show that our approach mitigates artifacts seen in Fourier reconstruction, including image blurring and degradation and ringing artifacts caused by windowing and channel cross-Talk. By demonstrating more accurate reconstructions, we push performance to the native resolution of the sensor, allowing more information to be recovered from a single measurement of a channeled linear imaging polarimeter.

Channeled linear imaging polarimeters measure the two-dimensional distribution of the linear Stokes parameters. A key aspect of this technique is to accurately reconstruct the Stokes parameters from a snapshot, modulated measurement of the channeled linear imaging polarimeter. The state-of-The-Art reconstruction takes the Fourier transform of the measurement to separate the Stokes parameters into channels. While straightforward, this approach is sensitive to channel cross-Talk and imposes bandwidth limitations that cut off high frequency details. To overcome these drawbacks, we present a reconstruction method called compressed channeled linear imaging polarimetry. In this framework, reconstruction in channeled linear imaging polarimetry is an underdetermined problem, where we measure N pixels and recover 3N Stokes parameters. We formulate an optimization problem by creating a mathematical model of the channeled linear imaging polarimeter with inspiration from compressed sensing. Through simulations, we show that our approach mitigates artifacts seen in Fourier reconstruction, including image blurring and degradation and ringing artifacts caused by windowing and channel cross-Talk. By demonstrating more accurate reconstructions, we push performance to the native resolution of the sensor, allowing more information to be recovered from a single measurement of a channeled linear imaging polarimeter.