Iterative Coordinate Descent Algorithm Research Articles

An Iterative Coordinate Descent Algorithm to Compute Sparse Low-Rank Approximations

In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz algorithm to build an approximate singular value decomposition for a few principal components. We show the performance of the proposed algorithm to recover sparse principal components on various datasets from the literature and perform dimensionality reduction for classification applications.

Power Minimization-Based Joint Task Scheduling and Resource Allocation in Downlink C-RAN

In this paper, we consider the network power minimization problem in a downlink cloud radio access network (C-RAN), taking into account the power consumed at the baseband unit (BBU) for computation and the power consumed at the remote radio heads and fronthaul links for transmission. The power minimization problem for transmission is a fast time-scale issue, whereas the power minimization problem for computation is a slow time-scale issue. Therefore, the joint network power minimization problem is a mixed time-scale problem. To tackle the time-scale challenge, we introduce large system analysis to turn the original fast time-scale problem into a slow time-scale one that only depends on the statistical channel information. In addition, we propose a bound improving branch-and-bound algorithm and a combinational algorithm to find the optimal and suboptimal solutions to the power minimization problem for computation, respectively, and propose an iterative coordinate descent algorithm to find the solutions to the power minimization problem for transmission. Finally, a distributed algorithm based on hierarchical decomposition is proposed to solve the joint network power minimization problem. In summary, this paper provides a framework to investigate how execution efficiency and computing capability at BBU as well as delay constraint of tasks can affect the network power minimization problem in C-RANs.

A Parallel Algorithm for Large-Scale Nonconvex Penalized Quantile Regression

ABSTRACTPenalized quantile regression (PQR) provides a useful tool for analyzing high-dimensional data with heterogeneity. However, its computation is challenging due to the nonsmoothness and (sometimes) the nonconvexity of the objective function. An iterative coordinate descent algorithm (QICD) was recently proposed to solve PQR with nonconvex penalty. The QICD significantly improves the computational speed but requires a double-loop. In this article, we propose an alternative algorithm based on the alternating direction method of multiplier (ADMM). By writing the PQR into a special ADMM form, we can solve the iterations exactly without using coordinate descent. This results in a new single-loop algorithm, which we refer to as the QPADM algorithm. The QPADM demonstrates favorable performance in both computational speed and statistical accuracy, particularly when the sample size n and/or the number of features p are large. Supplementary material for this article is available online.

Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method.

X-ray luminescence computed tomography (XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. Combining the principles of X-ray excitation of luminescence-based probes and optical signal detection, XLCT naturally fuses functional and anatomical images and provides complementary information for a wide range of applications in biomedical research. In order to improve the data acquisition efficiency of previously developed narrow-beam XLCT, a cone beam XLCT (CB-XLCT) mode is adopted here to take advantage of the useful geometric features of cone beam excitation. Practically, a major hurdle in using cone beam X-ray for XLCT is that the inverse problem here is seriously ill-conditioned, hindering us to achieve good image quality. In this paper, we propose a novel Bayesian method to tackle the bottleneck in CB-XLCT reconstruction. The method utilizes a local regularization strategy based on Gaussian Markov random field to mitigate the ill-conditioness of CB-XLCT. An alternating optimization scheme is then used to automatically calculate all the unknown hyperparameters while an iterative coordinate descent algorithm is adopted to reconstruct the image with a voxel-based closed-form solution. Results of numerical simulations and mouse experiments show that the self-adaptive Bayesian method significantly improves the CB-XLCT image quality as compared with conventional methods.

SU‐F‐I‐49: Vendor‐Independent, Model‐Based Iterative Reconstruction On a Rotating Grid with Coordinate‐Descent Optimization for CT Imaging Investigations

Purpose:Iterative reconstruction methods show promise for improving image quality and lowering the dose in helical CT. We aim to develop a novel model‐based reconstruction method that offers potential for dose reduction with reasonable computation speed and storage requirements for vendor‐independent reconstruction from clinical data on a normal desktop computer.Methods:In 2012, Xu proposed reconstructing on rotating slices to exploit helical symmetry and reduce the storage requirements for the CT system matrix. Inspired by this concept, we have developed a novel reconstruction method incorporating the stored‐system‐matrix approach together with iterative coordinate‐descent (ICD) optimization. A penalized‐least‐squares objective function with a quadratic penalty term is solved analytically voxel‐by‐voxel, sequentially iterating along the axial direction first, followed by the transaxial direction. 8 in‐plane (transaxial) neighbors are used for the ICD algorithm. The forward problem is modeled via a unique approach that combines the principle of Joseph's method with trilinear B‐spline interpolation to enable accurate reconstruction with low storage requirements. Iterations are accelerated with multi‐CPU OpenMP libraries. For preliminary evaluations, we reconstructed (1) a simulated 3D ellipse phantom and (2) an ACR accreditation phantom dataset exported from a clinical scanner (Definition AS, Siemens Healthcare). Image quality was evaluated in the resolution module.Results:Image quality was excellent for the ellipse phantom. For the ACR phantom, image quality was comparable to clinical reconstructions and reconstructions using open‐source FreeCT_wFBP software. Also, we did not observe any deleterious impact associated with the utilization of rotating slices. The system matrix storage requirement was only 4.5GB, and reconstruction time was 50 seconds per iteration.Conclusion:Our reconstruction method shows potential for furthering research in low‐dose helical CT, in particular as part of our ongoing development of an acquisition/reconstruction pipeline for generating images under a wide range of conditions. Our algorithm will be made available open‐source as “FreeCT_ICD”.NIH U01 CA181156; Disclosures (McNitt‐Gray): Institutional research agreement, Siemens Healthcare; Past recipient, research grant support, Siemens Healthcare; Consultant, Toshiba America Medical Systems; Consultant, Samsung Electronics

An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression

We propose and study a new iterative coordinate descent algorithm (QICD) for solving nonconvex penalized quantile regression in high dimension. By permitting different subsets of covariates to be relevant for modeling the response variable at different quantiles, nonconvex penalized quantile regression provides a flexible approach for modeling high-dimensional data with heterogeneity. Although its theory has been investigated recently, its computation remains highly challenging when p is large due to the nonsmoothness of the quantile loss function and the nonconvexity of the penalty function. Existing coordinate descent algorithms for penalized least-squares regression cannot be directly applied. We establish the convergence property of the proposed algorithm under some regularity conditions for a general class of nonconvex penalty functions including popular choices such as SCAD (smoothly clipped absolute deviation) and MCP (minimax concave penalty). Our Monte Carlo study confirms that QICD substantially improves the computational speed in the p ≫ n setting. We illustrate the application by analyzing a microarray dataset.

DF-based sum-rate optimization for multicarrier multiple access relay channel

We consider a system that consists of two sources, a half-duplex relay and a destination. The sources want to transmit their messages reliably to the destination with the help of the relay. We study and analyze the performance of a transmission scheme in which the relay implements a decode-and-forward strategy. We assume that all the channels are frequency selective, and in order to cope with that, we incorporate Orthogonal Frequency-Division Multiplexing (OFDM) transmission into the system. In contrast to previous works, both sources can transmit their messages using all subcarriers and the relay can decide to help none, only one, or both sources. For this scheme, we discuss the design criteria and evaluate the achievable sum-rate. Next, we study and solve the problem of resource allocation aiming at maximizing the achievable sum-rate. We propose an iterative coordinate-descent algorithm that finds a solution that is at least a local optimum. We show through numerical examples the effectiveness of the algorithms and illustrate the benefits of allowing both sources to transmit on all subcarriers.

Joint source-channel rate allocation and client clustering for scalable multistream IPTV.

We design a system framework for streaming scalable internet protocol television (IPTV) content to heterogenous clients. The backbone bandwidth is optimally allocated between source and parity data layers that are delivered to the client population. The assignment of stream layers to clients is done based on their access link data rate and packet loss characteristics, and is part of the optimization. We design three techniques for jointly computing the optimal number of multicast sessions, their respective source and parity rates, and client membership, either exactly or approximatively, at lower complexity. The latter is achieved via an iterative coordinate descent algorithm that only marginally underperforms relative to the exact analytic solution. Through experiments, we study the advantages of our framework over common IPTV systems that deliver the same source and parity streams to every client. We observe substantial gains in video quality in terms of both its average value and standard deviation over the client population. In addition, for energy efficiency, we propose to move the parity data generation part to the edge of the backbone network, where each client connects to its IPTV stream. We analytically study the conditions under which such an approach delivers energy savings relative to the conventional case of source and parity data generation at the IPTV streaming server. Finally, we demonstrate that our system enables more consistent streaming performance, when the clients' access link packet loss distribution is varied, relative to the two baseline methods used in our investigation, and maintains the same performance as an ideal system that serves each client independently.

A Model Based Iterative Reconstruction Algorithm For High Angle Annular Dark Field-Scanning Transmission Electron Microscope (HAADF-STEM) Tomography

High angle annular dark field (HAADF)-scanning transmission electron microscope (STEM) data is increasingly being used in the physical sciences to research materials in 3D because it reduces the effects of Bragg diffraction seen in bright field TEM data. Typically, tomographic reconstructions are performed by directly applying either filtered back projection (FBP) or the simultaneous iterative reconstruction technique (SIRT) to the data. Since HAADF-STEM tomography is a limited angle tomography modality with low signal to noise ratio, these methods can result in significant artifacts in the reconstructed volume. In this paper, we develop a model based iterative reconstruction algorithm for HAADF-STEM tomography. We combine a model for image formation in HAADF-STEM tomography along with a prior model to formulate the tomographic reconstruction as a maximum a posteriori probability (MAP) estimation problem. Our formulation also accounts for certain missing measurements by treating them as nuisance parameters in the MAP estimation framework. We adapt the iterative coordinate descent algorithm to develop an efficient method to minimize the corresponding MAP cost function. Reconstructions of simulated as well as experimental data sets show results that are superior to FBP and SIRT reconstructions, significantly suppressing artifacts and enhancing contrast.

An evaluation of cardiac uniformity, contrast, and SNR with dual-head 180/spl deg/ and triple-head 360/spl deg/ SPECT scans

An experimental phantom study was performed to evaluate cardiac uniformity, contrast, and signal-to-noise ratio for two clinical cardiac SPECT imaging protocols: adjacent dual-head 180/spl deg/ and triple-head 360/spl deg/ scans. One head of a SPECT camera was used to acquire 180/spl deg/ and 360/spl deg/ projections with different times per step to simulate the clinical case where dual-head 180/spl deg/ and triple-head 360/spl deg/ each takes a total of 20 min. Scans were acquired with no lesion, anterior lesion, and posterior lesion in the myocardium. Maximum a posteriori reconstruction was done by an iterative coordinate descent algorithm using a quadratic convex prior. The L-curve method was used to obtain the prior strength. Some investigation was done on obtaining the L-curve and on the ways to fit the L-curve and to get the corner point. Images both with attenuation and scatter correction (ASC) and without ASC were compared. The 180/spl deg/ scan shows an intensity decrease in anterior apical and posterior basal regions. The 360/spl deg/ scan shows an intensity decrease in the posterior wall. For the anterior lesion, the 180/spl deg/ scan has slightly better contrast, while for the posterior lesion, the 360/spl deg/ scan has slightly better contrast. The difference between the 180/spl deg/ and 360/spl deg/ scans is subtle, and the comparison results depend on the lesion position and the view angle of the heart. A receiver operating characteristic study of 180/spl deg/ versus 360/spl deg/ acquisition designed based on these characterizations of contrast, uniformity, and noise will be necessary to evaluate overall performance.