Vector Recovery Research Articles

A new multiple line outage identification formulation using a sparse vector recovery technique

This paper develops new methods to estimate the locations of transmission line outages in transmission networks. Two transmission outage models are developed based on DC and AC power flow equations and injected power changes due to line outages. The models are then generalized to include other transmission lines in addition to the outaged lines to provide a full representation of transmission networks. Three methods are developed based on the DC and AC models: Method_1 uses the DC power flow model; Method_2 uses the AC power flow model with zero line resistance; Method_3 uses the AC power flow model with line losses taken into account. A regularized least square based on ℓ1-norm minimization is developed to solve the models and estimate the locations of outages. Simulation results of the IEEE 39-, 57- and 118-bus systems verify the effectiveness of the developed methods in detecting line outage locations.

Geometric inference for general high-dimensional linear inverse problems

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence intervals and hypothesis testing. A theoretical framework is developed to characterize the local estimation rate of convergence and to provide statistical inference guarantees. Our results are built based on the local conic geometry and duality. The difficulty of statistical inference is captured by the geometric characterization of the local tangent cone through the Gaussian width and Sudakov estimate.

Frame Interpolation for Cloud-Based Mobile Video Streaming

Cloud-based High Definition (HD) video streaming is becoming popular day by day. On one hand, it is important for both end users and large storage servers to store their huge amount of data at different locations and servers. On the other hand, it is becoming a big challenge for network service providers to provide reliable connectivity to the network users. There have been many studies over cloud-based video streaming for Quality of Experience (QoE) for services like YouTube. Packet losses and bit errors are very common in transmission networks, which affect the user feedback over cloud-based media services. To cover up packet losses and bit errors, Error Concealment (EC) techniques are usually applied at the decoder/receiver side to estimate the lost information. This paper proposes a time-efficient and quality-oriented EC method. The proposed method considers H.265/HEVC based intra-encoded videos for the estimation of whole intra-frame loss. The main emphasis in the proposed approach is the recovery of Motion Vectors (MVs) of a lost frame in real-time. To boost-up the search process for the lost MVs, a bigger block size and searching in parallel are both considered. The simulation results clearly show that our proposed method outperforms the traditional Block Matching Algorithm (BMA) by approximately 2.5 dB and Frame Copy (FC) by up to 12 dB at a packet loss rate of 1%, 3%, and 5% with different Quantization Parameters (QPs). The computational time of the proposed approach outperforms the BMA by approximately 1788 seconds.

Successive Concave Sparsity Approximation for Compressed Sensing

In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the $\ell_0$ norm can be controlled. We prove that the series of the approximations asymptotically coincides with the $\ell_1$ and $\ell_0$ norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed which leads to a number of weighted $\ell_1$ minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms.

Exploiting joint sparsity in compressed sensing-based RFID

We propose a novel scheme to improve compressed sensing (CS)-based radio frequency identification (RFID) by exploiting multiple measurement vectors. Multiple measurement vectors are obtained by employing multiple receive antennas at the reader or by separation into real and imaginary parts. Our problem formulation renders the corresponding signal vectors jointly sparse, which in turn enables the utilization of CS. Moreover, the joint sparsity is exploited by an appropriate algorithm. We formulate the multiple measurement vector problem in CS-based RFID and demonstrate how a joint recovery of the signal vectors strongly improves the identification speed and noise robustness. The key insight is as follows: Multiple measurement vectors allow to shorten the CS measurement phase, which translates to shortened tag responses in RFID. Furthermore, the new approach enables robust signal support estimation and no longer requires prior knowledge of the number of activated tags.

Distribution systems state estimation using sparsified voltage profile

This paper exploits an electrical characteristic of distribution networks to cast the state estimation problem into a sparse vector recovery problem. In distribution networks, voltage differences between two buses of each line segment are much smaller than the infeed bus voltage. Therefore, the voltage profile signal can be sparsified with a difference transformation and recovered from only a few micro-phasor measurement units (μPMUs) using compressive sensing (CS) and ℓ1 regularization. The effectiveness of the proposed algorithm is verified through the simulation results of a standard unbalanced distribution network, the IEEE 123-bus system, under different operation conditions. The method accurately estimates system states even with multiple bad current measurements. It also detects, identifies, and corrects bad voltage measurements. In addition, a problem of binary integer linear programming is solved to obtain and optimally place the minimum number of μPMUs necessary to provide a unique solution for the proposed state estimation formulation.

Line outage identification-based state estimation in a power system with multiple line outages

Line outages in power systems cause data centers to miss some measurements thus making parts of networks unobservable. They also change the network topology and, consequently, classical state estimators do not converge. This paper proposes a new state estimation methodology based on the concepts of sparse vector recovery and line outage modeling. The proposed method first uses the pre- and post-outage voltage angle measurements to find the changes in network topology. Then it uses either the post-contingency data from PMUs and updated line flows or post-contingency measurements from PMUs and conventional PQ meters, as well as the updated topology, to provide an estimate of the power system state. The performance and accuracy of the proposed method are evaluated for the IEEE 24-, 57- and 118-bus systems. The simulation results show that the method provides good results for the three networks.

Robust surface normal estimation via greedy sparse regression

Photometric stereo (PST) is a widely used technique of estimating surface normals from an image set. However, it often produces inaccurate results for non-Lambertian surface reflectance. In this study, PST is reformulated as a sparse recovery problem where non-Lambertian errors are explicitly identified and corrected. We show that such a problem can be accurately solved via a greedy algorithm called orthogonal matching pursuit (OMP). The performance of OMP is evaluated on synthesized and real-world datasets: we found that the greedy algorithm is overall more robust to non-Lambertian errors than other state-of-the-art sparse approaches with little loss of efficiency. Along with providing an overview of current methods, novel contributions in this paper are as follows: we propose an alternative sparse formulation for PST; in previous PST studies (Wu et al., Robust photometric stereo via low-rank matrix completion and recovery, 2010), (S. Ikehata et al., Robust photometric stereo using sparse regression, 2012), the surface normal vector and the error vector are treated as two entities and are solved independently. In this study, we convert their formulation into a new canonical form of the sparse recovery problem by combining the two vectors into one large vector in a new “stacked” formulation in this domain. This allows for a large repertoire of existing sparse recovery algorithms to be more straightforwardly applied to the PST problem. In our application of the OMP greedy algorithm, we show that greedy solvers can indeed be applied, with this study supplying the first of such attempt at employing greedy approaches to estimate surface normals within the framework of PST. We numerically compare the performance of several normal vector recovery methods. Most notably, this is the first detailed test on complex images of the normal estimation accuracy of our previously proposed method, least median of squares (LMS).

Bayesian linear regression with sparse priors

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients that are significantly different from zero. The asymptotic shape of the posterior distribution is characterized and employed to the construction and study of credible sets for uncertainty quantification.

Distributed MIMO radar based on sparse sensing: Analysis and efficient implementation

In sparse sensing based distributed multiple-input multiple-output radars, the problem of target estimation is formulated as a sparse vector recovery problem, where the vector to be recovered is block sparse, or equivalently, the sensing matrix is block diagonal and the sparse vector consists of equal-length blocks that have the same sparsity profile. This paper derives the theoretical requirements and performance guarantees for the application of sparse recovery techniques to this problem. The obtained theoretical results confirm previous, simulations-based observations that exploiting the block sparsity of the target vector can further reduce the amount of measurements needed for successful target estimation. For signal recovery, two low-complexity approaches are proposed. The first one is an alternating direction method of multipliers-based sparse signal recovery algorithm, which in addition to significantly reducing computations is also amenable to a parallel and semidistributed implementation. The second approach decouples the location and speed estimation into two separate stages, with each stage addressing a sparse recovery problem of lower dimension while maintaining high estimation accuracy.

Sparse Localization with a Mobile Beacon Based on LU Decomposition in Wireless Sensor Networks

Node localization is the core in wireless sensor network. It can be solved by powerful beacons, which are equipped with global positioning system devices to know their location information. In this article, we present a novel sparse localization approach with a mobile beacon based on LU decomposition. Our scheme firstly translates node localization problem into a 1-sparse vector recovery problem by establishing sparse localization model. Then, LU decomposition pre-processing is adopted to solve the problem that measurement matrix does not meet the re- stricted isometry property. Later, the 1-sparse vector can be exactly recovered by compressive sensing. Finally, as the 1-sparse vector is approximate sparse, weighted Cen- troid scheme is introduced to accurately locate the node. Simulation and analysis show that our scheme has better localization performance and lower requirement for the mobile beacon than MAP+GC, MAP-M, and MAP-M&N schemes. In addition, the obstacles and DOI have little effect on the novel scheme, and it has great localization performance under low SNR, thus, the scheme proposed is robust.

Stability of the elastic net estimator

The elastic net is a regularized least squares regression method that has been widely used in learning and variable selection. The elastic net regularization linearly combines an l1 penalty term (like the lasso) and an l2 penalty term (like ridge regression). The l1 penalty term enforces sparsity of the elastic net estimator, whereas the l2 penalty term ensures democracy among groups of correlated variables. Compressed sensing is currently an extensively studied technique for efficiently reconstructing a sparse vector from much fewer samples/observations. In this paper we study the elastic net in the setting of sparse vector recovery. For recovering sparse vectors from few observations by employing the elastic net regression, we prove in this paper that the elastic net estimator is stable provided that the underlying measurement/design matrix satisfies the commonly required restricted isometry property or the sparse approximation property. It is well known that many independent random measurement matrices satisfy the restricted isometry property while random measurement matrices generated by highly correlated Gaussian random variables satisfy the sparse approximation property. As a byproduct, we establish a uniform bound for the grouping effect of the elastic net. Some numerical experiments are provided to illustrate our theoretical results on stability and grouping effect of the elastic net estimator.

Nested Periodic Matrices and Dictionaries: New Signal Representations for Period Estimation

In this paper, we propose a new class of techniques to identify periodicities in data. We target the period estimation directly rather than inferring the period from the signal’s spectrum. By doing so, we obtain several advantages over the traditional spectrum estimation techniques such as DFT and MUSIC. Apart from estimating the unknown period of a signal, we search for finer periodic structure within the given signal. For instance, it might be possible that the given periodic signal was actually a sum of signals with much smaller periods. For example, adding signals with periods 3, 7, and 11 can give rise to a period 231 signal. We propose methods to identify these “hidden periods” 3, 7, and 11. We first propose a new family of square matrices called Nested Periodic Matrices (NPMs), having several useful properties in the context of periodicity. These include the DFT, Walsh–Hadamard, and Ramanujan periodicity transform matrices as examples. Based on these matrices, we develop high dimensional dictionary representations for periodic signals. Various optimization problems can be formulated to identify the periods of signals from such representations. We propose an approach based on finding the least $l_{2}$ norm solution to an under-determined linear system. Alternatively, the period identification problem can also be formulated as a sparse vector recovery problem and we show that by a slight modification to the usual $l_{1}$ norm minimization techniques, we can incorporate a number of new and computationally simple dictionaries.

A Sparse Representation Approach to Online Estimation of Power System Distribution Factors

In this paper, we propose a method to compute linear sensitivity distribution factors (DFs) in near real time without relying on a power flow model of the system. Specifically, we compute the injection shift factors (ISFs) of a particular line of interest with respect to active power injections at all buses (all other DFs can be determined from ISFs). The proposed ISF estimation method relies on the solution of an underdetermined system of linear equations that arise from high-frequency synchronized measurements obtained from phasor measurement units. We exploit a sparse representation (i.e., one in which many elements are zero) of the vector of desired ISFs via rearrangement by electrical distance and an appropriately chosen linear transformation, and cast the estimation problem into a sparse vector recovery problem. As we illustrate through case studies, the proposed approach provides accurate DF estimates with fewer sets of synchronized measurements than earlier approaches that rely on the solution of an overdetermined system of equations via the least-squares errors estimation method.

Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries

In many applications, one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to the challenge, in a compressive sensing framework, one is given only an undersampled set of linear projections of the composite signal. In this study, the authors propose using the Dantzig selector model incorporating an overcomplete dictionary to separate a noisy undersampled collection of composite signals, and present an algorithm to efficiently solve the model. The Dantzig selector is a statistical approach to finding a solution to a noisy linear regression problem by minimising the l1 norm of candidate coefficient vectors while constraining the scope of the residuals. The Dantzig selector performs well in the recovery and separation of an unknown composite signal when the underlying coefficient vector is sparse. They propose a proximity operator-based algorithm to recover and separate unknown noisy undersampled composite signals using the Dantzig selector. They present numerical simulations comparing the proposed algorithm with the competing alternating direction method, and the proposed algorithm is found to be faster, while producing similar quality results. In addition, they demonstrate the utility of the proposed algorithm by applying it in various applications including the recovery of complex-valued coefficient vectors, the removal of impulse noise from smooth signals, and the separation and classification of a composition of handwritten digits.

461. Scale-Up and Manufacturing of High-Titer Foamy Virus Vector Containing Human CD18 for the Treatment of Leukocyte Adhesion Deficiency

Compared to other integrating viral vectors, foamy virus (FV) vectors have several distinct advantages as a gene transfer tool, including: the ability to carry larger expression cassettes, the increased stability due to a DNA genome formed in developing vector particles, and the random integration pattern without preference for promoter regions or active genes as is the case with gamma-retroviral and lentiviral vectors. In addition, the FV envelope has tropism for most cell types and is not associated with disease in humans. Combined, these properties make FV vectors the ideal candidate for gene therapy application. Proof of principle was provided by Bauer et al. (Nat. Med. 2008) showing cure of canine Leukocyte Adhesion Deficiency (LAD) using autologous CD34+ cells transduced with FV vector carrying the CD18 gene, without short or long-term adverse effects. Here we demonstrate the optimization of large scale manufacturing of FV vector carrying the human CD18 gene for the treatment of human LAD. As compared to the methods used in the canine LAD study, a 60-fold increase in FV-CD18 titer was observed using a combination of polyethylenimine (PEI) transfection and use of a codon-optimized gag, from approximately 1.70E+04 to 1.00E+06 Infectious Units/mL (IU/mL) on Raw 264.7 cells. An evaluation of purification strategies showed efficient vector purification and concentration of FV vector through a combination of heparin-affinity chromatography on the AKTA ready, a disposable fluid path chromatography unit, tangential flow filtration and ultracentrifugation, with an overall 5000-fold concentration and 20-30% recovery. This approach was compatible with large scale manufacturing in compliance with Good Manufacturing Practices (GMP). Although 5% DMSO is needed for optimal recovery of infectious FV vector from -80°C storage, highly concentrated vector can be diluted to reduce the DMSO concentration and toxicity to CD34+ cells, while maintaining effective transduction rates of up to 50%. This process is currently being finalized for clinical manufacturing in support of a Phase I trial for the treatment of LAD.Note: MN and DL equally contributed to this study.

A series of conditional shuttle vectors for targeted genomic integration in budding yeast.

The capacity of Saccharomyces cerevisiae to repair exposed DNA ends by homologous recombination has long been used by experimentalists to assemble plasmids from DNA fragments in vivo. While this approach works well for engineering extrachromosomal vectors, it is not well suited to the generation, recovery and reuse of integrative vectors. Here, we describe the creation of a series of conditional centromeric shuttle vectors, termed pXR vectors, that can be used for both plasmid assembly in vivo and targeted genomic integration. The defining feature of pXR vectors is that the DNA segment bearing the centromere and origin of replication, termed CEN/ARS, is flanked by a pair of loxP sites. Passaging the vectors through bacteria that express Cre recombinase reduces the loxP-CEN/ARS-loxP module to a single loxP site, thereby eliminating the ability to replicate autonomously in yeast. Each vector also contains a selectable marker gene, as well as a fragment of the HO locus, which permits targeted integration at a neutral genomic site. The pXR vectors provide a convenient and robust method to assemble DNAs for targeted genomic modifications.

Stability of low-rank matrix recovery and its connections to Banach space geometry

There are well-known relationships between compressed sensing and the geometry of the finite-dimensional ℓp spaces. A result of Kashin and Temlyakov [20] can be described as a characterization of the stability of the recovery of sparse vectors via ℓ1-minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional ℓ1 and ℓ2 spaces, whereas a more recent result of Foucart, Pajor, Rauhut and Ullrich [16] proves an analogous relationship even for ℓp spaces with p<1. In this paper we prove what we call matrix or noncommutative versions of these results: we characterize the stability of low-rank matrix recovery via Schatten p-(quasi-)norm minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional Schatten p-spaces.

Exact Safety Verification of Hybrid Systems Based on Bilinear SOS Representation

In this article, we address the problem of safety verification of nonlinear hybrid systems. A hybrid symbolic-numeric method is presented to compute exact inequality invariants of hybrid systems efficiently. Some numerical invariants of a hybrid system can be obtained by solving a bilinear SOS programming via the PENBMI solver or iterative method, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact polynomial invariants with rational coefficients, which exactly satisfy the conditions of invariants. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.

Simple downstream process based on detergent treatment improves yield and in vivo transduction efficacy of adeno-associated virus vectors

Recombinant adeno-associated viruses (rAAV) are promising candidates for gene therapy approaches. The last two decades were particularly fruitful in terms of processes applied in the production and purification of this type of gene transfer vectors. This rapid technological evolution led to better yields and higher levels of vector purity. Recently, some reports showed that rAAV produced by transient tri-transfection method in adherent human embryonic kidney 293 cells can be harvested directly from supernatant, leading to easier and faster purification compared to classical virus extraction from cell pellets. Here, we compare these approaches with new vector recovery method using small quantity of detergent at the initial clarification step to treat the whole transfected cell culture. Coupled with tangential flow filtration and iodixanol-based isopycnic density gradient, this new method significantly increases rAAV yields and conserves high vector purity. Moreover, this approach leads to the reduction of the total process duration. Finally, the vectors maintain their functionality, showing unexpected higher in vitro and in vivo transduction efficacies. This new development in rAAV downstream process once more demonstrates the great capacity of these vectors to easily accommodate to large panel of methods, able to furthermore ameliorate their safety, functionality, and scalability.