Dung N. Tran

High-speed flow microscopy using compressed sensing with ultrafast laser pulses.

We demonstrate an imaging system employing continuous high-rate photonically-enabled compressed sensing (CHiRP-CS) to enable efficient microscopic imaging of rapidly moving objects with only a few percent of the samples traditionally required for Nyquist sampling. Ultrahigh-rate spectral shaping is achieved through chirp processing of broadband laser pulses and permits ultrafast structured illumination of the object flow. Image reconstructions of high-speed microscopic flows are demonstrated at effective rates up to 39.6 Gigapixel/sec from a 720-MHz sampling rate.

Ultrawideband compressed sensing of arbitrary multi-tone sparse radio frequencies using spectrally encoded ultrafast laser pulses

We demonstrate a photonic system for pseudorandom sampling of multi-tone sparse radio-frequency (RF) signals in an 11.95-GHz bandwidth using <1% of the measurements required for Nyquist sampling. Pseudorandom binary sequence (PRBS) patterns are modulated onto highly chirped laser pulses, encoding the patterns onto the optical spectra. The pulses are partially compressed to increase the effective sampling rate by 2.07×, modulated with the RF signal, and fully compressed yielding optical integration of the PRBS-RF inner product prior to photodetection. This yields a 266× reduction in the required electronic sampling rate. We introduce a joint-sparsity-based matching-pursuit reconstruction via bagging to achieve accurate recovery of tones at arbitrary frequencies relative to the reconstruction basis.

An unsupervised dictionary learning algorithm for neural recordings

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. To further improve the reconstruction and classification performance, we proposed a joint prediction to determine the class of neural spikes in dictionary learning. When the neural spikes is compressed 50 times, our approach can achieve an average gain of 2 dB and 15 percentage units over state-of-the-art of CS approaches in terms of the reconstruction quality and classification accuracy respectively.

Sparse signal recovery based on nonconvex entropy minimization

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 and 2-dimensional real image recovery show that minimizing lp favors sparse solutions, and that it could recover sparse signals better than the convex l1 norm minimization and the nonconvex lp-norm minimization.

Low-rank matrices recovery via entropy function

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. In this paper, we introduce a new method that requires substantially fewer measurements needed for exact matrix recovery compared to nuclear norm minimization. The proposed optimization program utilizes a sparsity promoting regularization in the form of the entropy function of the singular values. Numerical experiments on synthetic and real data demonstrates that the proposed method outperforms stage-of-the-art nuclear norm minimization algorithms.

72 MHz A-scan optical coherence tomography using continuous high-rate photonically-enabled compressed sensing (CHiRP-CS)

Randomly spectrally patterned laser pulses acquire more information in each sample, allowing for increasing imaging speed independent of detector limitations.

Nonnegative matrix factorization with gradient vertex pursuit

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 solution: there exists a polytope, whose vertices consist of a few columns of the original matrix, covering the entire set of remaining columns. Our algorithm is greedy: it detects, at each iteration, a correct vertex until the entire polytope is identified. We evaluate the proposed algorithm on both synthetic and real hyperspectral data, and show its superior performance compared with other state-of-the-art greedy pursuit algorithms.

High-speed compressed sensing measurement using spectrally-encoded ultrafast laser pulses

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 signals under test from only a few percent of the measurements required for conventional Nyquist sampling, significantly relaxing the required analog-to-digital conversion bandwidth and amount of data storage.

A provable nonconvex model for factoring nonnegative matrices

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 under separable assumption which states that each data point is a convex combination of a few distinct data columns. We utilize the concentration of the entropy function and the ℓ∞ norm to concentrate the energy on the least number of latent variables. We prove that under the separability assumption, our proposed model robustly recovers data columns that generate the dataset, even when the data is corrupted by noise. We empirically justify the robustness of the proposed model and show that it is significantly more robust than the state-of-the-art separable NMF algorithms.

Compressive coding via random replicate mirror

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 number of input-output pairs and to reconstruct the scene from random subsampled measurements after calibration. Various experiments are performed to illustrate successful camera calibration and scene reconstruction from sensor output.