arXiv subjects

Xin Yuan

Publications and source records attributed to Xin Yuan.

251 records · Page 14Linked to original sources

arXiv2015

Convergence of the Generalized Alternating Projection Algorithm for Compressive Sensing

The convergence of the generalized alternating projection (GAP) algorithm is studied in this paper to solve the compressive sensing problem $\yv = \Amat \xv + \epsilonv$. By assuming that $\Amat\Amat\ts$ is invertible, we prove that GAP converges linearly within a certain range of step-size when the sensing matrix $\Amat$ satisfies restricted isometry property (RIP) condition of $δ_{2K}$, where $K$ is the sparsity of $\xv$. The theoretical analysis is extended to the adaptively iterative thresholding (AIT) algorithms, for which the convergence rate is also derived based on $δ_{2K}$ of the sensing matrix. We further prove that, under the same conditions, the convergence rate of GAP is faster than that of AIT. Extensive simulation results confirm the theoretical assertions.

cs.IT↗

arXiv2015

Compressive Sensing via Low-Rank Gaussian Mixture Models

We develop a new compressive sensing (CS) inversion algorithm by utilizing the Gaussian mixture model (GMM). While the compressive sensing is performed globally on the entire image as implemented in our lensless camera, a low-rank GMM is imposed on the local image patches. This low-rank GMM is derived via eigenvalue thresholding of the GMM trained on the projection of the measurement data, thus learned {\em in situ}. The GMM and the projection of the measurement data are updated iteratively during the reconstruction. Our GMM algorithm degrades to the piecewise linear estimator (PLE) if each patch is represented by a single Gaussian model. Inspired by this, a low-rank PLE algorithm is also developed for CS inversion, constituting an additional contribution of this paper. Extensive results on both simulation data and real data captured by the lensless camera demonstrate the efficacy of the proposed algorithm. Furthermore, we compare the CS reconstruction results using our algorithm with the JPEG compression. Simulation results demonstrate that when limited bandwidth is available (a small number of measurements), our algorithm can achieve comparable results as JPEG.

stat.ML↗

arXiv2015

Lensless Compressive Imaging

We develop a lensless compressive imaging architecture, which consists of an aperture assembly and a single sensor, without using any lens. An anytime algorithm is proposed to reconstruct images from the compressive measurements; the algorithm produces a sequence of solutions that monotonically converge to the true signal (thus, anytime). The algorithm is developed based on the sparsity of local overlapping patches (in the transformation domain) and state-of-the-art results have been obtained. Experiments on real data demonstrate that encouraging results are obtained by measuring about 10% (of the image pixels) compressive measurements. The reconstruction results of the proposed algorithm are compared with the JPEG compression (based on file sizes) and the reconstructed image quality is close to the JPEG compression, in particular at a high compression rate.

cs.CV↗

arXiv2015

Non-Gaussian Discriminative Factor Models via the Max-Margin Rank-Likelihood

We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A discriminative factor model is then developed, integrating the max-margin rank-likelihood and (linear) Bayesian support vector machines, which are also built on the max-margin principle. The discriminative factor model is further extended to the {\em nonlinear} case through mixtures of local linear classifiers, via Dirichlet processes. Fully local conjugacy of the model yields efficient inference with both Markov Chain Monte Carlo and variational Bayes approaches. Extensive experiments on benchmark and real data demonstrate superior performance of the proposed model and its potential for applications in computational biology.

stat.ML↗

arXiv2015

The influence of the broadness of the degree distribution on network's robustness: comparing localized attack and random attack

The stability of networks is greatly influenced by their degree distributions and in particular by their broadness. Networks with broader degree distributions are usually more robust to random failures but less robust to localized attacks. To better understand the effect of the broadness of the degree distribution we study here two models where the broadness is controlled and compare their robustness against localized attacks (LA) and random attacks (RA). We study analytically and by numerical simulations the cases where the degrees in the networks follow a Bi-Poisson distribution $P(k)=αe^{-λ_1}\frac{λ_1^k}{k!}+(1-α) e^{-λ_2}\frac{λ_2^k}{k!},α\in[0,1]$, and a Gaussian distribution $P(k)=A \cdot exp{(-\frac{(k-μ)^2}{2σ^2})}$ with a normalization constant $A$ where $k\geq 0$. In the Bi-Poisson distribution the broadness is controlled by the values of $α$, $λ_1$ and $λ_2$, while in the Gaussian distribution it is controlled by the standard deviation, $σ$. We find that only for $α=0$ or $α=1$, namely degrees obeying a pure Poisson distribution, LA and RA are the same but for all other cases networks are more vulnerable under LA compared to RA. For Gaussian distribution, with an average degree $μ$ fixed, we find that when $σ^2$ is smaller than $μ$ the network is more vulnerable against random attack. However, when $σ^2$ is larger than $μ$ the network becomes more vulnerable against localized attack. Similar qualitative results are also shown for interdependent networks.

physics.soc-ph↗

arXiv2015

A Generative Model for Deep Convolutional Learning

A generative model is developed for deep (multi-layered) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up (pretraining) and top-down (refinement) probabilistic learning. Experimental results demonstrate powerful capabilities of the model to learn multi-layer features from images, and excellent classification results are obtained on the MNIST and Caltech 101 datasets.

stat.ML↗

arXiv2015

Generative Deep Deconvolutional Learning

A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning. After learning the deep convolutional dictionary, testing is implemented via deconvolutional inference. To speed up this inference, a new statistical approach is proposed to project the top-layer dictionary elements to the data level. Following this, only one layer of deconvolution is required during testing. Experimental results demonstrate powerful capabilities of the model to learn multi-layer features from images. Excellent classification results are obtained on both the MNIST and Caltech 101 datasets.

stat.ML↗

arXiv2015

Compressive Hyperspectral Imaging with Side Information

A blind compressive sensing algorithm is proposed to reconstruct hyperspectral images from spectrally-compressed measurements.The wavelength-dependent data are coded and then superposed, mapping the three-dimensional hyperspectral datacube to a two-dimensional image. The inversion algorithm learns a dictionary {\em in situ} from the measurements via global-local shrinkage priors. By using RGB images as side information of the compressive sensing system, the proposed approach is extended to learn a coupled dictionary from the joint dataset of the compressed measurements and the corresponding RGB images, to improve reconstruction quality. A prototype camera is built using a liquid-crystal-on-silicon modulator. Experimental reconstructions of hyperspectral datacubes from both simulated and real compressed measurements demonstrate the efficacy of the proposed inversion algorithm, the feasibility of the camera and the benefit of side information.

cs.CV↗

arXiv2014

Tree-Structure Bayesian Compressive Sensing for Video

A Bayesian compressive sensing framework is developed for video reconstruction based on the color coded aperture compressive temporal imaging (CACTI) system. By exploiting the three dimension (3D) tree structure of the wavelet and Discrete Cosine Transformation (DCT) coefficients, a Bayesian compressive sensing inversion algorithm is derived to reconstruct (up to 22) color video frames from a single monochromatic compressive measurement. Both simulated and real datasets are adopted to verify the performance of the proposed algorithm.

cs.CV↗

arXiv2014

Coherent Sources Direction Finding and Polarization Estimation with Various Compositions of Spatially Spread Polarized Antenna Arrays

Various compositions of sparsely polarized antenna arrays are proposed in this paper to estimate the direction-of-arrivals (DOAs) and polarizations of multiple coherent sources. These polarized antenna arrays are composed of one of the following five sparsely-spread sub-array geometries: 1) four spatially-spread dipoles with three orthogonal orientations, 2) four spatially-spread loops with three orthogonal orientations, 3) three spatially-spread dipoles and three spatially-spread loops with orthogonal orientations, 4) three collocated dipole-loop pairs with orthogonal orientations, and 5) a collocated dipole-triad and a collocated loop-triad. All the dipoles/loops/pairs/triads in each sub-array can also be sparsely spaced with the inter-antenna spacing far larger than a half-wavelength. Only one dimensional spatial-smoothing is used in the proposed algorithm to derive the two-dimensional DOAs and polarizations of multiple cross-correlated signals. From the simulation results, the sparse array composed of dipole-triads and loop-triads is recommended to construct a large aperture array, while the sparse arrays composed of only dipoles or only loops are recommended to efficiently reduce the mutual coupling across the antennas. Practical applications include distributed arrays and passive radar systems.

physics.ins-det↗

arXiv2014

Low-Cost Compressive Sensing for Color Video and Depth

A simple and inexpensive (low-power and low-bandwidth) modification is made to a conventional off-the-shelf color video camera, from which we recover {multiple} color frames for each of the original measured frames, and each of the recovered frames can be focused at a different depth. The recovery of multiple frames for each measured frame is made possible via high-speed coding, manifested via translation of a single coded aperture; the inexpensive translation is constituted by mounting the binary code on a piezoelectric device. To simultaneously recover depth information, a {liquid} lens is modulated at high speed, via a variable voltage. Consequently, during the aforementioned coding process, the liquid lens allows the camera to sweep the focus through multiple depths. In addition to designing and implementing the camera, fast recovery is achieved by an anytime algorithm exploiting the group-sparsity of wavelet/DCT coefficients.

cs.CV↗

arXiv2014

Multiscale Shrinkage and Lévy Processes

A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$ corresponds to the coefficients of a wavelet or block-DCT representation of data. The method we consider in detail, and for which numerical results are presented, is based on increments of a gamma process. However, we demonstrate that the general framework is appropriate for many other types of shrinkage priors, all within the Lévy process family, with the gamma process a special case. Bayesian inference is carried out by approximating the posterior with samples from an MCMC algorithm, as well as by constructing a heuristic variational approximation to the posterior. We also consider expectation-maximization (EM) for a MAP (point) solution. State-of-the-art results are manifested for compressive sensing and denoising applications, the latter with spiky (non-Gaussian) noise.

stat.ML↗

arXiv2013

Adaptive Temporal Compressive Sensing for Video

This paper introduces the concept of adaptive temporal compressive sensing (CS) for video. We propose a CS algorithm to adapt the compression ratio based on the scene's temporal complexity, computed from the compressed data, without compromising the quality of the reconstructed video. The temporal adaptivity is manifested by manipulating the integration time of the camera, opening the possibility to real-time implementation. The proposed algorithm is a generalized temporal CS approach that can be incorporated with a diverse set of existing hardware systems.

stat.AP↗

arXiv2013

Polynomial-Phase Signal Direction-Finding & Source-Tracking with an Acoustic Vector Sensor

A new ESPRIT-based algorithm is proposed to estimate the direction-of-arrival of an arbitrary degree polynomial-phase signal with a single acoustic vector sensor. The proposed approach requires neither a priori knowledge of the polynomial-phase signal's coefficients nor a priori knowledge of the polynomial-phase signal's frequency-spectrum. A pre-processing technique is also proposed to incorporate the single-forgetting-factor algorithm and multiple-forgetting-factor adaptive tracking algorithm to track a polynomial-phase signal using one acoustic vector sensor. Simulation results verify the efficacy of the proposed direction finding and source tracking algorithms.

stat.AP↗

arXiv2013

Joint DOA and Polarization Estimation with Sparsely Distributed and Spatially Non-Collocating Dipole/Loop Triads

This paper introduces an ESPRIT-based algorithm to estimate the directions-of-arrival and polarizations for multiple sources. The investigated algorithm is based on new sparse array geometries, which are composed of three non-collocating dipole triads or three non-collocating loop triads. Both the inter-triad spacings and the inter-sensor spacings in the same triad can be far larger than a half-wavelength of the incident sources. By adopting the ESPRIT algorithm, the eigenvalues of the data-correlation matrix offer the fine but ambiguous estimates of the direction-cosines for each source, and the eigenvectors provide the estimates of each source's steering vector. Based on the constrained array geometries, the fine and unambiguous estimates of directions-of-arrival and polarizations are obtained. Simulation results verify the efficacy of the investigated approach and also verify the aperture extension property of the proposed array geometries.

stat.AP↗

arXiv2013

Coded aperture compressive temporal imaging

We use mechanical translation of a coded aperture for code division multiple access compression of video. We present experimental results for reconstruction at 148 frames per coded snapshot.

cs.CV↗

arXiv2012

Phonon-induced dephasing of chromium colour centres in diamond

We report on the coherence properties of single photons from chromium-based colour centres in diamond. We use field-correlation and spectral lineshape measurements to reveal the interplay between slow spectral wandering and fast dephasing mechanisms as a function of temperature. We show that the zero-phonon transition frequency and its linewidth follow a power-law dependence on temperature indicating that the dominant fast dephasing mechanisms for these centres are direct electron-phonon coupling and phonon-modulated Coulomb coupling to nearby impurities. Further, the observed reduction in the quantum yield for photon emission as a function of temperature is consistent with the opening of additional nonradiative channels through thermal activation to higher energy states predominantly and indicates a near-unity quantum efficiency at 4 K.

cond-mat.mes-hall↗