In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using dictionary learning. We then perform an SVD on the dictionary and use the first few left singular vectors as the rows of the measurement matrix to obtain the compressive measurements for reconstruction. The proposed method provides significant improvement over the conventional compressive sensing approaches. The reconstruction performance is further improved by reconditioning the sensing matrix using matrix balancing. We also demonstrate that the combination of dictionary learning and SVD is robust by applying them to different datasets.
Based on compressive sampling techniques and short exposure imaging, super-resolution imaging with thermal light is experimentally demonstrated exploiting the sparse prior property of images for standard conventional imaging system. Differences between super-resolution imaging demonstrated in this letter and super-resolution ghost imaging via compressive sampling (arXiv. Quant-ph/0911.4750v1 (2009)), and methods to further improve the imaging quality are also discussed.
For ghost imaging, pursuing high resolution images and short acquisition times required for reconstructing images are always two main goals. We report an image reconstruction algorithm called compressive sampling (CS) reconstruction to recover ghost images. By CS reconstruction, ghost imaging with both super-resolution and a good signal-to-noise ratio can be obtained via short acquisition times. Both effect influencing and approaches further improving the resolution of ghost images via CS reconstruction, relationship between ghost imaging and CS theory are also discussed.
Coded aperture snapshot spectral imaging (CASSI) is a promising technique to capture the three-dimensional hyperspectral image (HSI) using a single coded two-dimensional (2D) measurement, in which algorithms are used to perform the inverse problem. Due to the ill-posed nature, various regularizers have been exploited to reconstruct the 3D data from the 2D measurement. Unfortunately, the accuracy and computational complexity are unsatisfied. One feasible solution is to utilize additional information such as the RGB measurement in CASSI. Considering the combined CASSI and RGB measurement, in this paper, we propose a new fusion model for the HSI reconstruction. We investigate the spectral low-rank property of HSI composed of a spectral basis and spatial coefficients. Specifically, the RGB measurement is utilized to estimate the coefficients, meanwhile the CASSI measurement is adopted to provide the orthogonal spectral basis. We further propose a patch processing strategy to enhance the spectral low-rank property of HSI. The proposed model neither requires non-local processing or iteration, nor the spectral sensing matrix of the RGB detector. Extensive experiments on both simulated and real HSI dataset demonstrate that our proposed method outperforms previous state-of-the-art not only in quality but also speeds up the reconstruction more than 5000 times.
Much more image details can be resolved by improving the systems imaging resolution and enhancing the resolution beyond the systems Rayleigh diffraction limit is generally called super-resolution. By combining the sparse prior property of images with the ghost imaging method, we demonstrated experimentally that super-resolution imaging can be nonlocally achieved in the far field even without looking at the object. Physical explanation of super-resolution ghost imaging via compressive sampling and its potential applications are also discussed.
Multilinear Compressive Learning (MCL) is an efficient signal acquisition and learning paradigm for multidimensional signals. The level of signal compression affects the detection or classification performance of a MCL model, with higher compression rates often associated with lower inference accuracy. However, higher compression rates are more amenable to a wider range of applications, especially those that require low operating bandwidth and minimal energy consumption such as Internet-of-Things (IoT) applications. Many communication protocols provide support for adaptive data transmission to maximize the throughput and minimize energy consumption. By developing compressive sensing and learning models that can operate with an adaptive compression rate, we can maximize the informational content throughput of the whole application. In this paper, we propose a novel optimization scheme that enables such a feature for MCL models. Our proposal enables practical implementation of adaptive compressive signal acquisition and inference systems. Experimental results demonstrated that the proposed approach can significantly reduce the amount of computations required during the training phase of remote learning systems but also improve the informational content throughput via adaptive-rate sensing.