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We study the Nonnegative Matrix Factorization problem which approximates a nonnegative matrix by a low-rank factorization. This problem is particularly important in Machine Learning, and finds itself in a large number of applications. Unfortunately, the original formulation is ill-posed and NP-hard. In this paper, we propose a row sparse model based on Row Entropy Minimization to solve the NMF problem...
Randomly spectrally patterned laser pulses acquire more information in each sample, allowing for increasing imaging speed independent of detector limitations.
We develop a Compressive Sensing (CS) imaging system that uses titled reflective sub-apertures placed at random angles to create replicates of random placement and orientation within the image plane and a variation adopting the beam splitter. We derive efficient methods based on sparse recovery to calibrate the transfer function of the camera from a set of calibrating images, which allows the reducing...
We propose a new sparsity-promoting objective function to be used in sparse signal recovery. Specifically, the objective is an entropy function 𝑙1 defined on the sparse signal x. Compared to the conventional 𝑙1, it is a nonconvex function and the optimization problem can be solved based on the fast iterative shrinkage thresholding algorithm (FISTA). Experiments on 1-dimensional sparse signal recovery...
The low-rank matrix recovery problem consists of reconstructing an unknown low-rank matrix from a few linear measurements, possibly corrupted by noise. One of the most popular method in low-rank matrix recovery is based on nuclear-norm minimization, which seeks to simultaneously estimate the most significant singular values of the target low-rank matrix by adding a penalizing term on its nuclear norm...
We experimentally demonstrate a photonic RF sampling system that utilizes chirp processing of ultrafast laser pulses to achieve all-optical high-rate pseudorandom patterning and inner product integration for compressed sensing measurement. We successfully acquire multi-tone sparse radio frequency (RF) signals at arbitrary offsets from the reconstruction basis frequencies in an 11.95 GHz bandwidth...
In this paper, we study Locally Compressed Sensing for images, where sampling process is allowed to be performed on arbitrary local regions of the images. We propose a fast and efficient reconstruction algorithm which utilizes local structures of images. Several numerical experiments on real images demonstrates that our algorithm yields better reconstruction quality than existing techniques at much...
We demonstrate 119.2-GSample/s compressive microwave frequency detection using spectrally-encoded ultrafast laser pulses. We sense sparse tones over > 35-GHz instantaneous bandwidth with 2-MHz accuracy using < 300 consecutive compressive measurements acquired at a 400-MHz rate.
To meet the growing demand of wireless and power efficient neural recordings systems, we demonstrate an unsupervised dictionary learning algorithm in Compressed Sensing (CS) framework which can be implemented in VLSI systems. Without prior label information of neural spikes, we extend our previous work to unsupervised learning and construct a dictionary with discriminative structures for spike sorting...
Nonnegative Matrix Factorization (NMF), defined as factorizing a nonnegative matrix into two nonnegative factor matrices, is a particularly important problem in machine learning. Unfortunately, it is also ill-posed and NP-hard. We propose a fast, robust, and provably correct algorithm, namely Gradient Vertex Pursuit (GVP), for solving a well-defined instance of the problem which results in a unique...
We present a chirp processing technique for encoding pseudorandom patterns onto the spectra of broadband optical pulses for compressed sensing (CS) measurement. We demonstrate applications to characterization of ultrawideband sparse radio frequency (RF) signals and to very high-speed continuous microscopic flow imaging. In both domains, the optical sampling technique permits accurate recovery of the...
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