Iterative Projection Algorithm Research Articles

Computationally-Efficient Overdetermined Blind Source Separation Based on Iterative Source Steering

This paper describesa computationally-efficient optimization algorithm for the blind source separation (BSS) of overdetermined mixtures. In the determined case, a matrix-inversion-free iterative source steering (ISS) algorithm has been proposed for estimating a square demixing matrix as a computationally-efficient alternative to the popular iterative projection (IP) algorithm. The IP algorithm is based on source-wise (i.e., row-wise) updates of the demixing matrix, and lends itself naturally to an extension to overdetermined independent vector analysis (IVA) called OverIVA. In contrast, the ISS algorithm changes the whole demixing matrix at every update, making its extension to the overdetermined case non-trivial. In this paper, we propose a modified ISS algorithm for OverIVA fully exploiting the computational savings of ISS. We also derive an overdetermined extension of independent low-rank matrix analysis (OverILRMA) with the modified ISS algorithm. Experimental results showed that the proposed ISS-based OverIVA and OverILRMA were comparable or superior to the conventional IP-based counterparts in speech separation performance while achieving lower computational cost.

Convolutive Transfer Function-Based Multichannel Nonnegative Matrix Factorization for Overdetermined Blind Source Separation

Most multichannel blind source separation (BSS) approaches rely on a spatial model to encode the transfer functions from sources to microphones and a source model to encode the source power spectral density. The rank-1 spatial model has been widely exploited in independent component analysis (ICA), independent vector analysis (IVA), and independent low-rank matrix analysis (ILRMA). The full-rank spatial model is also considered in many BSS approaches, such as full-rank spatial covariance matrix analysis (FCA), multichannel nonnegative matrix factorization (MNMF), and FastMNMF, which can improve the separation performance in the case of long reverberation times. This paper proposes a new MNMF framework based on the convolutive transfer function (CTF) for overdetermined BSS. The time-domain convolutive mixture model is approximated by a frequency-wise convolutive mixture model instead of the widely adopted frequency-wise instantaneous mixture model. The iterative projection algorithm is adopted to estimate the demixing matrix, and the multiplicative update rule is employed to estimate nonnegative matrix factorization (NMF) parameters. Finally, the source image is reconstructed using a multichannel Wiener filter. The advantages of the proposed method are twofold. First, the CTF approximation enables us to use a short window to represent long impulse responses. Second, the full-rank spatial model can be derived based on the CTF approximation and slowly time-variant source variances, and close relationships between the proposed method and ILRMA, FCA, MNMF and FastMNMF are revealed. Extensive experiments show that the proposed algorithm achieves a higher separation performance than ILRMA and FastMNMF in reverberant environments.

Convergence results for stochastic convex feasibility problem using random Mann and simultaneous projection iterative algorithms in Hilbert space

Real life problems are entrenched in ambiguities. To deal with these ambiguities, stochastic functional analysis has emerged as one of the mathematical tools for solving these kinds of problems. The purpose of this paper is to extend the convergence results of deterministic convex feasibility problems to a stochastic convex feasibility problem and prove that the solution of a convex feasibility problem generated by random Mann-type and Simultaneous projection iterative algorithms with firmly non-expansive mapping converge in quadratic mean and consequently in probability to random fixed point in Hilbert space. These results extend, unify, and generalize different established deterministic results in the literature.

Generalized optimization framework for pixel super-resolution imaging in digital holography.

The imaging quality of in-line digital holography is challenged by the twin-image and aliasing effects because sensors only respond to intensity and pixels are of finite size. As a result, phase retrieval and pixel super-resolution techniques serve as two essential ingredients for high-fidelity and high-resolution holographic imaging. In this work, we combine the two as a unified optimization problem and propose a generalized algorithmic framework for pixel-super-resolved phase retrieval. In particular, we introduce the iterative projection algorithms and gradient descent algorithms for solving this problem. The basic building blocks, namely the projection operator and the Wirtinger gradient, are derived and analyzed. As an example, the Wirtinger gradient descent algorithm for pixel-super-resolved phase retrieval, termed as Wirtinger-PSR, is proposed and compared with the classical error-reduction algorithm. The Wirtinger-PSR algorithm is verified with both simulated and experimental data. The proposed framework generalizes well to various physical settings and helps bridging the gap between empirical studies and theoretical analyses.

Image reconstruction of electrical capacitance tomography based on optimal simulated annealing algorithm using orthogonal test method

Electrical capacitance tomography (ECT) is a visualization measurement method for two-phase flow. Imaging permittivity distributions using electrical capacitance tomography has always been one of the most significant issues studied by scholars, and the algorithm will have a great impact on the accuracy of image reconstruction result. This paper applies simulated annealing (SA) algorithm to image reconstruction in ECT. However, some parameters of SA algorithm need to be optimized in order to obtain better reconstructed images in ECT. The influence of different parameter values in SA algorithm for image reconstruction in ECT is studied, and a set of optimal parameters of the SA algorithm is obtained based on the orthogonal experimental design method in this paper. At the same time, simulation and static experiments are conducted. Reconstructed images by SA algorithm with optimized parameter are compared with the linear back projection (LBP) and Landweber iterative algorithms. The results show that better images can be obtained for typical oil-gas two-phase flow using SA algorithm. The quality and shape fidelity of reconstructed image for the central object are obviously improved.

A convergence analysis for iterative sparsification projection with soft-thresholding

The recently proposed iterative sparsification projection (ISP), a fast and robust sparse signal recovery algorithm framework, can be classified as smooth-ISP and nonsmooth-ISP. However, no convergence analysis has been established for the nonsmooth-ISP in the previous works. Motivated by this absence, the present paper provides a convergence analysis for ISP with soft-thresholding (ISP-soft) which is an instance of the nonsmooth-ISP. In our analysis, the composite operator of soft-thresholding and proximal projection is viewed as a fixed point mapping, whose nonexpansiveness plays a key role. Specifically, our convergence analysis for the sequence generated by ISP-soft can be summarized as follows: 1) For each inner loop, we prove that the sequence has a unique accumulation point which is a fixed point, and show that it is a Cauchy sequence; 2) for the last inner loop, we prove that the accumulation point of the sequence is a critical point of the objective function if the final value of the threshold satisfies a condition, and show that the corresponding objective values are monotonically nonincreasing. A numerical experiment is given to validate some of our results and intuitively present the convergence.

Event-triggered learning consensus of networked heterogeneous nonlinear agents with switching topologies

In this work, a lifted event-triggered iterative learning control (lifted ETILC) is proposed aiming for addressing all the key issues of heterogeneous dynamics, switching topologies, limited resources, and model-dependence in the consensus of nonlinear multi-agent systems (MASs). First, we establish a linear data model for describing the I/O relationships of the heterogeneous nonlinear agents as a linear parametric form to make the non-affine structural MAS affine with respect to the control input. Both the heterogeneous dynamics and uncertainties of the agents are included in the parameters of the linear data model, which are then estimated through an iterative projection algorithm. On this basis, a lifted event-triggered learning consensus is proposed with an event-triggering condition derived through a Lyapunov function. In this work, no threshold condition but the event-triggering condition is used which plays a key role in guaranteeing both the stability and the iterative convergence of the proposed lifted ETILC. The proposed method can reduce the number of control actions significantly in batches while guaranteeing the iterative convergence of tracking error. Both rigorous analysis and simulations are provided and confirm the validity of the lifted ETILC.

Two-dimensional iterative projection method for subsample speckle tracking of ultrasound images.

Speckle tracking provides robust motion estimation necessary to create accurate post-processed images. These methods are known to be less accurate in the lateral dimension compared with the axial dimension due to the limitations on the lateral resolution of ultrasound scanning. This paper proposes a two-dimensional iterative projection (TDIP) algorithm using the Riesz transform to generate the analytic signals. The TDIP is an improvement to an already accurate speckle tracking algorithm called the phase coupled (PC) method. The PC method projects the intersection of gradients on the correlation map to the zero phase contour to estimate displacement. The TDIP method performs iterative projections and uses the aggregate of these projected locations to estimate the motion, in addition to rejecting inaccurate projections by checking them against the aggregate projection location. The TDIP additionally adopts the Riesz transform to generate two-dimensional analytic signals to improve lateral accuracy. The Riesz transform is a multidimensional extension of the Hilbert transform into the nD Euclidean space and therefore can be used to include data in both axial and lateral dimensions as opposed to the commonly used Hilbert transform which is one dimensional. The accuracy of the TDIP is quantitatively proven on simulated datasets from the Field II simulation program and on experimental data from two flow phantoms. At all cases, the TDIP is more accurate than the PC algorithm at two-dimensional displacement estimation. Graphical Abstract The lateral estimates from the Phase Coupled algorithm. This method uses the Hilbert transform for the analytic signal. There is large estimated motion within the flow blockage bounded by the red, fin shape in the center of the flow channel. The flow channel itself is also bounded by dashed, red lines. Graphical Abstract The lateral estimates from the TDIP method. This method is not tracking motion within the blockage in the center of the flow channel. The channel and the blockage are both bounded by dashed, red lines.

The energy management strategies based on dynamic energy pricing for community integrated energy system considering the interactions between suppliers and users

The proliferation of cogeneration technology, information and communication technology has facilitated the integrations of different energy infrastructures and markets. In this paper, the energy management of an integrated energy system composed of multiple energy hub operators and numerous integrated energy providers is formulated as dynamic energy pricing problem. From the perspective of maximizing social welfare, a distributed gradient projection iterative algorithm is proposed to decide the dynamic energy prices and optimal operation strategies of all the participants. Furthermore, the dual decomposition method is employed to decouple the coupled constraints and the primal problem is decomposed into several independent subproblems which can be solved in a distributed manner without violating privacy. Simulation results indicate that the proposed energy pricing algorithm shows a good convergence and availability, which can guarantee the supply-demand balance in each time slot, as well as promote the interactions between the energy supply and consumption sides.

Feasible Region: An Actuation-Aware Extension of the Support Region

In legged locomotion, the projection of the robot's Center of Mass (CoM) being inside the convex hull of the contact points is a commonly accepted sufficient condition to achieve static balancing. However, some of these configurations cannot be realized because the joint-torques required to sustain them would be above their limits (actuation limits). In this article, we rule out such configurations and define the feasible region, a revisited support region that guarantees both global static stability in the sense of tip-over and slippage avoidance and of existence of a set of joint-torques that are able to sustain the robot's body weight. We show that the feasible region can be employed for the online selection of feasible footholds and CoM trajectories to achieve statically stable locomotion on rough terrains, also in presence of load-intensive tasks. Key results of our approach include the efficiency in the computation of the feasible region using an Iterative Projection (IP) algorithm and the successful execution of hardware experiments on the HyQ robot, that was able to negotiate obstacles of moderate dimensions while carrying an extra 10-kg payload.

A PRIMARY EXPLORATION ON THE SUPER-NETWORK MODEL OF ECONOMIC DEVELOPMENT UNDER THE RESTRICTION OF RESOURCES AND ENVIRONMENT

With the theory of super-network and the variational inequality method, this paper establishes a super-network model of economic development in three aspects, builds a new indicator system for measuring economic development, and calculates the equilibrium conditions for the balance of economic development. Firstly, the economic development is divided into three parts: economic growth, ecological environment optimization and scientific and technological progress. Respectively, with the set of measuring indicators in three aspects as a point of super-network and the link between these indicators as a super edge, thus a super-network model is established. Secondly, the hierarchical variable clustering analysis method is used to analyze the tightness of the links among the nodes in the super-network; and the objective function is established by using the partial measurement index, which simplifies the model. Finally, the variational inequality and projection iterative algorithm are used to calculate the equilibrium condition of the whole model. The main conclusions in this paper are as follows: (1) The indicators of economic development are interrelated with each other. (2) It can contribute to the balanced development of the economy in satisfied certain conditions.

High-order compact scheme finite difference discretization for Signorini's problem

This paper brings out an analysis of the projection iterative algorithm for the numerical solution of the Signorini problem. The very closed connections with the switching method are highlighted. In addition, the relevance of higher-order discretization for Signorini problem is discussed. Thus, a specific iterative solver is developed to address the present fourth and sixth-order compact scheme discretizations. This method is based on a lower-order preconditioning method. Several numerical experiments have been performed to bring light to the accuracy of such method, despite the lack of smoothness at the Signorini boundary.

Semi-Average Sampling for Shift-Invariant Signals in a Mixed Lebesgue Space

This article mainly studies the nonuniform and semi-average sampling of time-varying shift-invariant signals living in a mixed Lebesgue space under the condition that the generator of the shift-invariant subspace belongs to a hybrid-norm space of mixed form depending on the orders p and q. First, the sampling stability for two kinds of semi-average sampling functionals is established. Then, we give the corresponding iterative approximation projection algorithms with exponential convergence for recovering the time-based shift-invariant signals from the semi-average samples.

Diagonally Dominant Principal Component Analysis

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the “diagonally dominant principal component analysis (DD-PCA).” DD-PCA is an effective tool for designing statistical methods for strongly correlated data. We showcase the use of DD-PCA in two statistical problems: covariance matrix estimation and global detection in multiple testing. Using the output of DD-PCA, we propose a new estimator for estimating a large covariance matrix with factor structure. Thanks to a nice property of diagonally dominant matrices, this estimator enjoys the advantage of simultaneous good estimation of the covariance matrix and the precision matrix (by a plain inversion). A plug-in of this estimator to linear discriminant analysis and portfolio optimization yields appealing performance in real data. We also propose two new tests for testing the global null hypothesis in multiple testing when the z-scores have a factor covariance structure. Both tests first use DD-PCA to adjust the individual p-values and then plug in the adjusted p-values to the higher criticism (HC) test. These new tests significantly improve over the HC test and compare favorably with other existing tests. For computation of DD-PCA, we propose an iterative projection algorithm and an ADMM algorithm. Supplementary materials for this article are available online.

Average sampling and reconstruction of reproducing kernel signals in mixed Lebesgue spaces

In this paper, we mainly study the average sampling and reconstruction of signals in a reproducing kernel subspace of the mixed Lebesgue space Lp,q(Rm+n). First, the sampling stability for two kinds of average sampling functionals is considered. Then, the corresponding iterative approximation projection algorithms with exponential convergence are established. Finally, the asymptotic pointwise error estimates are given for reconstructing a signal from its average samples corrupted by additive random noise.

New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications

Some new inertial forward-backward projection iterative algorithms are designed in a real Hilbert space. Under mild assumptions, some strong convergence theorems for common zero points of the sum of two kinds of infinitely many accretive mappings are proved. New projection sets are constructed which provide multiple choices of the iterative sequences. Some already existing iterative algorithms are demonstrated to be special cases of ours. Some inequalities of metric projection and real number sequences are widely used in the proof of the main results. The iterative algorithms have also been modified and extended from pure discussion on the sum of accretive mappings or pure study on variational inequalities to that for both, which complements the previous work. Moreover, the applications of the abstract results on nonlinear capillarity systems are exemplified.

Исследование масштабируемости алгоритма Чиммино для решения систем линейных неравенств на кластерных вычислительных системах

The paper is devoted to a scalability study of Cimmino algorithm for linear inequality systems. This algorithm belongs to the class of iterative projection algorithms. For the analytical analysis of the scalability, the BSF (Bulk Synchronous Farm) parallel computation model is used. An implementation of the Cimmino algorithm in the form of operations on lists using higher-order functions Map and Reduce is presented. An analytical estimation of the upper scalability bound of the algorithm for cluster computing systems is derived. Information about the implementation of Cimmino algorithm on lists in C++ language using the BSF program skeleton and MPI parallel programming library is given. The results of large-scale computational experiments performed on a cluster computing system are demonstrated. A conclusion about the adequacy of the analytical estimations by comparing them with the results of computational experiments is made.

Direct Phasing of Protein Crystals with Non-Crystallographic Symmetry

An iterative projection algorithm proposed previously for direct phasing of high-solvent-content protein crystals is extended to include non-crystallographic symmetry (NCS) averaging. For proper NCS, when the NCS axis is positioned, the molecular envelope can be automatically rebuilt. For improper NCS, when the NCS axis and the translation vector are known, the molecular envelope can also be automatically reconstructed. Some structures with a solvent content of around 50% could be directly solved using this ab initio phasing method. Trial calculations are described to illustrate the methodology. Real diffraction data are used and the calculated phases are good for automatic model building. The refinement of approximate NCS parameters is discussed.

Ab initio phasing of the diffraction of crystals with translational disorder.

To date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed. In addition, the Bragg reflections alone are typically insufficient (by a factor of two) to determine the structure ab initio, and so prior information is required. Crystals formed from an imperfect packing of the protein molecules may also exhibit continuous diffraction between and beyond these Bragg reflections. When this is due to random displacements of the molecules from each crystal lattice site, the continuous diffraction provides the necessary information to determine the protein structure without prior knowledge, to a resolution that is not limited by the angular extent of the observed Bragg reflections but instead by that of the diffraction as a whole. This article presents an iterative projection algorithm that simultaneously uses the continuous diffraction as well as the Bragg reflections for the determination of protein structures. The viability of this method is demonstrated on simulated crystal diffraction.

How accurate and precise are CT based measurements of iodine concentration? A comparison of the minimum detectable concentration difference among single source and dual source dual energy CT in a phantom study.

To assess the impact of scan- and patient-related factors on the error and the minimum detectable difference in iodine concentration among different generations of single-source (SS) fast kV-switching and dual-source (DS) dual-energy CT (DECT). Lesions having eight different iodine concentrations (0.2-4 mgI/mL) were emulated in a 3D-printed phantom of medium and large size. Each combination of concentration and size was scanned in dual-energy mode on four different SS and DS DECTs. Radiation doses were 7 and 10 mGy (medium size) and 10, 13, and 16 mGy (large size). Iodine maps were reconstructed with filtered back projection (FBP) and vendor-specific iterative reconstruction algorithms (IRs). Absolute error of iodine quantification (E) was measured. Multivariate regression models determined the influence of CT scanner, iodine concentration, phantom size, radiation dose, and reconstruction algorithm on E. The minimum detectable difference in iodine concentration (ICmin) under the same imaging conditions (intra-conditional) and among different imaging conditions (inter-conditional) was calculated. The error was significantly lower in current than in previous DECT generations (p < 0.001). For all CT scanner conditions, the error was significantly higher with increasing phantom size and decreasing radiation dose (p < 0.001). Iodine concentration only significantly affected the error for SS DECT (p < 0.001). ICmin depended on patient- and scan-related factors and ranged from 0.4 to 1.5 mgI/mL. Patient- and scan-related factors have a significant impact on the error and minimum detectable difference in iodine concentration within and among SS fast kV-switching and DS DECT. • Patient- and scan-related factors have a significant impact on the error and minimum detectable difference in dual-energy CT-based iodine quantification. • Third-generation DECTs outperformed second-generation scanners for both single-source and dual-source dual-energy CT. • The minimum intra- and inter-conditional detectable difference in iodine concentration ranged from 0.4 to 1.5 mg iodine/mL.