Piecewise Autoregressive Research Articles

Virtual view synthesis for the nonuniform illuminated between views in surgical video

For high-quality surgical video virtual view synthesis, a Weighted Autoregressive Interpolation (WAI) algorithm and an Adaptively-enhanced Hole Filling (AHF) are proposed to reduce the artifacts caused by up-sampling and relieve the luma difference. First, high quality up-sampled reference views are acquired by the WAI algorithm. A Piecewise Autoregressive (PAR) model is introduced and the distance weight of pixels is also considered. The precision of the virtual view is improved by the WAI and the texture edges are well preserved. Next, for the AHF, the intermediate view with more structure details is selected as the template. The other intermediate view is calibrated to it. And the luma difference is relieved. Then, a Nearest background Holes Filling algorithm (NHF) is adopted to blend these two intermediate views, in which only background pixels are selected to fill the remaining holes. Combining the WAI with AHF, the visual quality of the surgical virtual video is improved. For the objective quality, the experimental results show that the PSNR of the proposed algorithm is 0.5841 dB higher than the VSRS 1D-Fast algorithm on average. For subjective quality, the proposed method can reduce the artifacts and gain higher subjective quality for the synthesized virtual view of the surgical video.

Predicting the air temperature of a building zone by detecting different configurations using a switched system identification technique

Considerable efforts have been made to find a reliable model able to accurately describe and predict the thermal behavior of the indoor environment of a building. Such a model is essential, in particular, for designing climate control strategies for optimizing both the comfort level and the energy consumption. However, a building is a complex system characterized by a nonlinear thermal behavior, so the task to find such a reliable model is rather difficult. This paper aims at overcoming some of these difficulties by presenting a data driven approach based on a switched system identification to detect and model the thermal behavior of a building zone during normal usage. The proposed technique relies on a PieceWise AutoRegressive model with eXogeneous inputs (PWARX) consisting of a set of sub-models with each one of them describing a certain configuration/state of the dwelling, e.g. turning the heating ON/OFF or opening/closing windows, doors and shutters. The approach is data-driven, easy to implement and its computational time is inferior to creating a detailed model under a specialized software. Therefore, it is particularly suitable for providing a quick description of the thermal behavior of existing buildings for which it is possible to install sensors and perform measurements. Using the available measurements, the algorithm is able to detect various configurations as will be shown by two numerical examples. Such a collection of sub-models provides a better temperature estimate than using ARX models, so it will eventually allow to select better strategies for improving energy efficiency.

Piecewise affine identification of a hydraulic pumping system using evolutionary computation

Identification of piecewise affine hybrid systems is not an easy task since both the parameters determining the discrete modes and the submodels parameters have to be obtained, leading to a non-convex combinatorial optimisation problem. One way around this problem is to solve it in two steps. This work presents an approach for simultaneously estimating the parameters for PieceWise Autoregressive eXogeneous and PieceWise Output Error models. This is accomplished by using evolutionary algorithms for finding the parameters of the discrete modes (Gaussian mixture models) and employing the proposed weighted and extended least squares algorithm to estimate the ARX or ARMAX submodels. The main advantages of the proposed algorithm are: (i) it can be applied to output error models - which correspond to system with measurement noise, (ii) it is less likely to get trapped in local minima and (iii) it is applicable to problems with large datasets. The proposed approach, which is offline, was validated using simulated and experimental data and was compared with another method from the literature. In the case of an experimental plant, parsimonious models with good performance in both dynamic and static regimes were obtained.

Identification and control of nonlinear systems using PieceWise Auto-Regressive eXogenous models

In this paper, we consider the problems of nonlinear system representation and control. In fact, we propose a solution based on PieceWise Auto-Regressive eXogenous (PWARX) models since these models are able to approximate any nonlinear behaviour with arbitrary precision. Moreover, the identification and control approaches of linear systems can be extended to these models because the parameters of each sub-model are linearly related to the output. The proposed solution is based on two steps. The first allows to represent the nonlinear system by a PWARX model using the identification approach. The second consists in designing a controller for each sub-model using the pole placement strategy. Simulation and experimental results are presented to illustrate the performance of the proposed approach.

On consistency of minimum description length model selection for piecewise autoregressions

The Auto-PARM (Automatic Piecewise AutoRegressive Modeling) procedure, developed by Davis et al. (2006), uses the minimum description length (MDL) principle to estimate the number and locations of structural breaks in a non-stationary time series. Consistency of this model selection procedure has been established when using conditional maximum (Gaussian) likelihood variance estimates. In contrast, the estimate of the number of change-points is inconsistent in general if Yule–Walker variance estimates are used instead. This surprising result is due to an exact cancellation of first-order terms in a Taylor series expansion in the conditional maximum likelihood case, which does not occur in the Yule–Walker case. In order to simplify notation and make the arguments more transparent, we only treat in detail the simple case where the time series follows an AR(p) model with no change-points.

Discrete event estimation of nonlinear hybrid dynamical systems using fuzzy clustering

Nonlinear hybrid dynamical systems change its continuous nonlinear dynamic due to occurrence of discrete events. In many applications of hybrid mechanical systems, discrete dynamic exists due to the change in magnitude of displacement and velocity which change its continuous dynamics. For model-based control of such systems, it is difficult to obtain first principle models due to unknown discrete events. In this work, clustering based fuzzy validation criteria is proposed to estimate the number of discrete event present in the hybrid mechanical systems along with identification of PieceWise Auto Regressive eXogenous model. The simulation results, on a mechanical hybrid system consist of discrete dynamics due to the magnitude of the velocity, which has nonlinear boundaries, are used to validate the proposed methodology.

SAR Imaging With Structural Sparse Representation

Sparse representation (SR)-based SAR imaging approaches have shown their superior performance compared with conventional approaches. However, for an image with rich spatial structures, a fixed global dictionary is usually ineffective to characterize the local structures. Piecewise autoregressive (PAR) model indicates that each pixel can be linearly represented by its local neighboring pixels. Inspired by this, an adaptive sparse space, effectively characterizing the varying image local structures, is designed, in which the entries are derived from the PAR model. By incorporating the adaptive SR into the SAR imaging, a novel structural SR-based SAR (SSR-SAR) imaging approach is proposed. Due to the fact that the adaptive sparse space is greatly dependent on the prior information of the SAR image, updating of the adaptive sparse space and SAR imaging is a joint optimization problem. In our approach, we propose to introduce the alternative minimization scheme to solve the problem. Besides, the Augmented Lagrangian Multiplier technique is adopted to accelerate the computation speed. Finally, experimental results are shown to demonstrate the validity of the proposed approach.

Parameter identification of PWARX models using fuzzy distance weighted least squares method

PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input–output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method.

A semi-batch reactor modeling based on PWARX systems

In this paper, we address the problem of identifying a semi-batch olive oil esterification reactor. In fact, this reactor can be considered as a PieceWise AutoRegressive eXogenous (PWARX) system. The Chiu's clustering procedure for the identification of PWARX systems is then applied. It consists in estimating both the parameter vector of each submodel and the coefficients of each partition. The results of the experimental validation illustrate the effectiveness of the proposed method. A comparative study with three existing approaches is also considered in this paper which shows that the proposed approach gives the best results in terms of precision.

An experimental validation of a novel clustering approach to PWARX identification

In this paper, the problem of clustering based procedure for the identification of PieceWise Auto-Regressive eXogenous (PWARX) models is addressed. This problem involves both the estimation of the parameters of the affine sub-models and the hyperplanes defining the partitions of the state-input regression. In fact, we propose the use of the Chiu's clustering algorithm in order to overcome the main drawbacks of the existing methods which are the poor initialization and the presence of outliers. In addition, our approach is able to generate automatically the number of sub-models. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to an olive oil esterification reactor is also suggested in order to validate simulation results.

Nonlocally Adaptive Pattern Classification Based Compressed Sensing for Video Recovery

Traditional video coding algorithms usually undergo several coding steps for each frame before transmission, which reduces the efficiency at the encoder. The compressed sensing (CS) as an innovative method in signal processing can make the encoder much easier than ever before, with which each frame only needs to multiply a projection matrix at the encoder, if the frame is sparse in a transform domain. Frames in a video usually exhibit sparsity in different parts on different bases; however, existing compressed sensing reconstruction methods usually recover a frame in a fixed set of bases for the entirety of the frame. Therefore, the frames cannot be recovered faithfully by the conventional CS reconstruction methods from a small number of measurements. In this paper, in order to rectify the flaw, we construct an initial estimation frame by motion estimation from neighboring frames and through the observation of the current frame. Then, nonlocally adaptive sparse signal presentation facilitation by a 2D piecewise autoregressive (AR) model is integrated into the reconstruction. The piecewise AR model is generated from the pattern classification of subimages of the initial estimation frame and its neighboring frames. An iterative procedure is proposed to recover a new estimated frame and its AR model alternatively, until the termination threshold is satisfied. The experimental results demonstrating the capabilities of the proposed method are presented.

Model-based adaptive resolution upconversion of degraded images

Resolution upconversion of a degraded image is an ill-posed inverse problem that is even harder than video superresolution due to lack of redundant observations from reference frames. To overcome this difficulty an adaptive 2D piecewise autoregressive (PAR) model is used to strengthen the constraints on the solution of the inverse problem. The PAR model can be fit to local image waveforms by adjusting its parameters. But estimating the model parameters needs the knowledge of the very original high-resolution pixels to be estimated by the model. We resolve this chicken-and-egg dilemma by adaptive nonlinear least-squares joint estimation of both model parameters and original pixels. This non-linear estimation problem is solved by the method of structured total least-squares, constrained by the degradation function (e.g., the point spread function of a camera plus noises) that forms the observed low-resolution image. As such, this work offers a unified general framework for joint upsampling, deconvolution, and denoising. Moreover, the upsampling can be carried out at an arbitrary scale rather than power of two. Experiments show that the proposed NEARU technique outperforms current methods in both PSNR and subjective visual quality, and its advantage becomes greater for larger scaling factors.

Super-resolution texture synthesis using stochastic PAR/NL model

Super-resolution texture synthesis using a locally-adaptive stochastic signal model is investigated in this work. The 2D random texture is modeled by a piecewise auto-regressive (PAR) process whose parameters are determined by a non-local (NL) training procedure and, consequently, it is called the PAR/NL model. Unlike previous work that applies the NL scheme to image pixels directly, the proposed PAR/NL scheme applies the NL scheme to PAR model parameters by assuming that these parameters are self-similar. Furthermore, we describe a probabilistic method for PAR/NL model computation using the maximum a posteriori (MAP) and the expectation–maximization (EM) principles. Experimental results are given to demonstrate the synthesis performance of the proposed PAR/NL technique, which can boost texture detail and eliminate the blurring artifact perceptually.

2A1-Q07 ハイブリッドシステムモデルに基づくモデル予測型前方車追突回避アシストシステムの設計(【交通・物流部門】自動車分野におけるロボティクス)

This paper presents verifications of proposed personalized assisting control using an actual car. A single-seated small electric vehicle is used to log driver's behavior in vehicle following tasks. Driver model is expressed as a PieceWise AutoRegressive eXogeneous(PWARX) model widely recognized as hybrid dynamical system. First, the braking assistance system with the model is designed and examined on a driving simulator. The optimum assisting control is based on model predictive control and given by solving Mixed Integer Programming(MIP) on-line. After implementation of the assistance system on the electric vehicle, it is aimed to verify the effect by comparing actual car's and simulated results.

Structural Break Estimation for Nonstationary Time Series Models

This article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive (AR) processes. The number and locations of the piecewise AR segments, as well as the orders of the respective AR processes, are assumed unknown. The minimum description length principle is applied to compare various segmented AR fits to the data. The goal is to find the “best” combination of the number of segments, the lengths of the segments, and the orders of the piecewise AR processes. Such a “best” combination is implicitly defined as the optimizer of an objective function, and a genetic algorithm is implemented to solve this difficult optimization problem. Numerical results from simulation experiments and real data analyses show that the procedure has excellent empirical properties. The segmentation of multivariate time series is also considered. Assuming that the true underlying model is a segmented autoregression, this procedure is shown to be consistent for estimating the location of the breaks.