Search results for: Yue M. Lu
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IEEE Transactions on Image Processing > 2017 > 26 > 11 > 5107 - 5121
Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized, so that each row sums to unity. Surprisingly, if we apply a column normalization before the row normalization, the performance of the smoothing filter can often be significantly improved. Prior works showed that such performance...
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We study a simple spectral method that serves as a key ingredient in a growing line of work using efficient iterative algorithms for estimating signals in nonconvex settings. Unlike previous work, which focuses on the phase retrieval setting and provides only bounds on the performance, we consider arbitrary generalized linear sensing models and provide an exact characterization of the performance...
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Solving a large-scale regularized linear inverse problem using multiple processors is important in various real-world applications due to the limitations of individual processors and constraints on data sharing policies. This paper focuses on the setting where the matrix is partitioned column-wise. We extend the algorithmic framework and the theoretical analysis of approximate message passing (AMP),...
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We study the dynamics of an online algorithm for learning a sparse leading eigenvector from samples generated from a spiked covariance model. This algorithm combines the classical Oja's method for online PCA with an element-wise nonlinearity at each iteration to promote sparsity. In the high-dimensional limit, the joint empirical measure of the underlying sparse eigenvector and its estimate provided...
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IEEE Transactions on Power Systems > 2016 > 31 > 5 > 3804 - 3815
We propose a fully distributed Gauss-Newton algorithm for state estimation of electric power systems. At each Gauss-Newton iteration, matrix-splitting techniques are utilized to carry out the matrix inversion needed for calculating the Gauss-Newton step in a distributed fashion. In order to reduce the communication burden as well as increase robustness of state estimation, the proposed distributed...
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IEEE Signal Processing Letters > 2016 > 23 > 9 > 1183 - 1187
Estimating low-rank positive-semidefinite (PSD) matrices from symmetric rank-one measurements is of great importance in many applications, such as high-dimensional data processing, quantum state tomography, and phase retrieval. When the rank is known a priori, this problem can be regarded as solving a system of quadratic equations of a low-dimensional subspace. The authors develop a fast iterative...
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Optimal power flow (OPF) seeks the operation point of a power system that maximizes a given objective function and satisfies operational and physical constraints. Given real-time operating conditions and the large scale of the power system, it is demanding to develop algorithms that allow for OPF to be decomposed and efficiently solved on parallel computing systems. In our work, we develop a parallel...
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IEEE Signal Processing Letters > 2016 > 23 > 3 > 346 - 350
Standard convolution as a model of radiometric degradation is in majority of cases inaccurate as the blur varies in space and we are thus required to work with a computationally demanding space-variant model. Space-variant degradation can be approximately decomposed to a set of standard convolutions. We explain in detail the properties of the space-variant degradation operator and show two possible...
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We present a novel algorithm — ProSparse Denoise — that can solve the sparsity recovery problem in the presence of noise when the dictionary is the union of Fourier and identity matrices. The algorithm is based on a proper use of Cadzow routine and Prony's method and exploits the duality of Fourier and identity matrices. The algorithm has low complexity compared to state of the art algorithms for...
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NeuroImage > 2016 > 125 > C > 587-600
Motivated by recent progress in signal processing on graphs, we have developed a matched signal detection (MSD) theory for signals with intrinsic structures described by weighted graphs. First, we regard graph Laplacian eigenvalues as frequencies of graph-signals and assume that the signal is in a subspace spanned by the first few graph Laplacian eigenvectors associated with lower eigenvalues. The...
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IEEE Transactions on Signal Processing > 2016 > 64 > 1 > 189 - 202
We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations. Central to our algorithm is a generalization of the annihilating filter method, a tool widely used in array signal processing and finite-rate-of-innovation (FRI) sampling. The proposed algorithm can reconstruct spikes from spatial samples...
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We propose an algorithm for blind calibration of multi-channel samplers in the presence of unknown gains and offsets, which is useful in many applications such as multi-channel analog-to-digital converters, image super-resolution, and sensor networks. Using a subspace-based rank condition developed by Vandewalle et al., we obtain a set of linear equations with respect to complex harmonics whose frequencies...
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We study a class of smoothing filters for image denoising. Expressed as matrices, these smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if one applies a column normalization to the matrix before the row normalization, the denoising quality can often be significantly improved. This column-row normalization corresponds to one iteration of a symmetrization process...
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We study phase retrieval by using a simple non-convex algorithm based on iterative projections. Our main contribution in this work is to establish an exact analysis of the dynamics of the algorithm in an online setting, with Gaussian measurement vectors. We show that the algorithm dynamics, measured by the squared distance between the current estimate and the true solution, can be fully characterized...
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Chromatic aberration, caused by photographic lens imperfections, results in the image of only one spectral channel being sharp, while the other channels are blurred depending on their wavelengths difference with the sharp channel. We study chromatic aberration for a system that jointly records color and near-infrared (NIR) images on a single sensor. Chromatic aberration in such a system leads to a...
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We provide a complete characterization of the randomized Kaczmarz algorithm (RKA) for inconsistent linear systems. The Kaczmarz algorithm, known in some fields as the algebraic reconstruction technique, is a classical method for solving large-scale overdetermined linear systems through a sequence of projection operators; the randomized Kaczmarz algorithm is a recent proposal by Strohmer and Vershynin...
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The problem of finding the sparse representation of a signal has attracted a lot of attention over the past years. In particular, uniqueness conditions and reconstruction algorithms have been established by relaxing a non-convex optimisation problem. The finite rate of innovation (FRI) theory is an alternative approach that solves the sparsity problem using algebraic methods based around Prony's algorithm...
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We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations. The proposed algorithm can reconstruct K spikes from (K + √K)2 spatial samples, thus improving over previously known FRI sampling schemes on the sphere by a factor of up to four. Further, we show how multiple sound source localization (SSL) by a spherical...
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Recent advances in materials, devices and fabrication technologies have motivated a strong momentum in developing solid-state sensors that can detect individual photons in space and time. It has been envisioned that such sensors can eventually achieve very high spatial resolutions (e.g., 109 pixels/chip) as well as high frame rates (e.g., 106 frames/sec). In this paper, we present an efficient algorithm...
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The Kaczmarz method, or the algebraic reconstruction technique (ART), is a popular method for solving large-scale overdetermined systems of equations. Recently, Strohmer et al. proposed the randomized Kaczmarz algorithm, an improvement that guarantees exponential convergence to the solution. This has spurred much interest in the algorithm and its extensions. We provide in this paper an exact formula...
