Efficient implementation of image interpolation as an inverse problem

This paper presents three computationally efficient solutions for the image interpolation problem which are developed in a general framework. This framework is based on dealing with the problem as an inverse problem. Based on the observation model, our objective is to obtain a high resolution image which is as close as possible to the original high resolution image subject to certain constraints. In the first solution, a linear minimum mean square error (LMMSE) approach is suggested. The necessary assumptions required to reduce the computational complexity of the LMMSE solution are presented. The sensitivity of the LMMSE solution to these assumptions is studied. In the second solution, the concept of entropy maximization of the required high resolution image a priori is used. The implementation of the suggested maximum entropy solution as a single sparse matrix inversion is presented. Finally, the well-known regularization technique used in iterative nature in image interpolation and image restoration is revisited. An efficient sectioned implementation of regularized image interpolation, which avoids the large number of iterations required in the interactive technique, is presented. In our suggested regularized solution, the computational time is linearly proportional to the dimensions of the image to be interpolated and a single matrix inversion of moderate dimensions is required. This property allows its implementation in interpolating images of any dimensions which is a great problem in iterative techniques. The effect of the choice of the regularization parameter on the suggested regularized image interpolation solution is studied. The performance of all the above-mentioned solutions is compared to traditional polynomial based interpolation techniques such as cubic O-MOMS and to iterative interpolation as well. The suitability of each solution to interpolating different images is also studied.     

Approximation-theoretic methods for nonlinear deconvolution and inversion

Nonlinear deconvolution and nonlinear inversion are cast as inverse problems in generalized Fock spaces. Generalized Fock spaces, introduced by de Figueiredo and Dwyer in [1], are reproducing kernel Hilbert spaces (RKHSs) of input-output maps represented by Volterra series equipped with an appropriately weighted inner product, the choice of the weights in the inner product depending on the particular problem under consideration. The solution to the nonlinear deconvolution problem presented here is the same as the one obtained previously for the nonlinear system identification problem [1–4]. However, the present solution to the nonlinear inversion problem consists of a new approach, whereby the unknown samples of the input are obtained from the given samples of the output by means of an efficient sequential algorithm. The algorithm is based on a framework which interpolates the input samples by an appropriate spline, and its sequential nature is elicited by the use of a truncated function basis to represent the spline.     

Application of artificial neural networks to solve problems of identification and determination of concentration of salts in multi-component water solutions by Raman spectra

In this paper, the results of elaboration and comparative analysis of approaches concerned with application of neural network algorithms for effective solution of problem of pattern recognition (inverse problem with discrete output) along with inverse problem with continuous output are presented. Consideration is carried out at the example of problem of identification and determination of concentrations of inorganic salts in multi-component water solutions by Raman spectra. The studied approach is concerned with solution of both problems (classification and determination of concentrations) using a single neural network trained on experimental or quasi-model data.     

Closed-Form Inverse Kinematics for Continuum Manipulators

This paper presents a novel, analytical approach to solving inverse kinematics for multi-section continuum robots, defined as robots composed of a continuously bendable backbone. The problem is decomposed into several simpler subproblems. First, this paper presents a solution to the inverse kinematics problem for a single-section trunk. Assuming endpoints for all sections of a multi-section trunk are known, this paper then details applying single-section inverse kinematics to each section of the multi-section trunk by compensating for the resulting changes in orientation. Finally, an approach which computes per-section endpoints given only a final-section endpoint provides a complete solution to the multi-section inverse kinematics problem. The results of implementing these algorithms in simulation and on a prototype continuum robot are presented and possible applications discussed.     

一种新的离散系统最优闭环极点配置方法

分析了LQ逆问题解的存在条件,以便合理选择期望的闭环极点,使之成为一组最优极点．提 出了一种以离散系统LQ逆问题分析为基础的新的最优控制系统设计方法,得到了开环、闭环 特征多项式系数与加权矩阵之间的解析关系,只要给定一组期望闭环极点,即可确定与 之对应的加权矩阵Q和R,从而得到一个具有指定极点的最优控制系统．     

Comparison of RBF and MLP neural networks to solve inverse kinematic problem for 6R serial robot by a fusion approach

In this paper, a fusion approach to determine inverse kinematics solutions of a six degree of freedom serial robot is proposed. The proposed approach makes use of radial basis function neural network for prediction of incremental joint angles which in turn are transformed into absolute joint angles with the assistance of forward kinematics relations. In this approach, forward kinematics relations of robot are used to obtain the data for training of neural network as well to estimate the deviation of predicted inverse kinematics solution from the desired solution. The effectiveness of the fusion process is shown by comparing the inverse kinematics solutions obtained for an end-effector of industrial robot moving along a specified path with the solutions obtained from conventional neural network approaches as well as iterative technique. The prominent features of the fusion process include the accurate prediction of inverse kinematics solutions with less computational time apart from the generation of training data for neural network with forward kinematics relations of the robot.     

WINSTODEC: a stochastic deconvolution interactive program for physiological and pharmacokinetic systems.

Deconvolution allows the reconstruction of non-accessible inputs (e.g. hormone secretion rate) from their causally-related measurable effects (e.g. hormone plasma concentration). Deconvolution is challenging under several aspects both general (e.g. determination of a suitable trade-off between data fit and solution smoothness in order to contrast ill-conditioning, assessment of the confidence intervals) as well as specific of physiological systems (e.g. non-uniform and infrequent data sampling). Recently, a stochastic regularization approach has been proposed and validated to handle these difficulties (De Nicolao et al., Automatica 33 (1997) 851-870). In this paper, an interactive program, WINSTODEC, is presented to allow the clinical investigator to easily obtain the solution of a deconvolution problem by this approach.     

Reliability-based approach to the inverse kinematics solution of robots using Elman's networks

The solution of inverse kinematics problem of redundant manipulators is a fundamental problem in robot control. The inverse kinematics problem in robotics is the determination of joint angles for a desired cartesian position of the end effector. For the solution of this problem, many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. Furthermore, many neural network approaches have been done to this problem. But the neural network-based solutions are not much reliable due to the error at the end of learning. Therefore, a reliability-based neural network inverse kinematics solution approach has been presented, and applied to a six-degrees of freedom (dof) robot manipulator in this paper. The structure of the proposed method is based on using three networks designed parallel to minimize the error of the whole system. Elman network, which has a profound impact on the learning capability and performance of the network, is chosen and designed according to the proposed solution method. At the end of parallel implementation, the results of each network are evaluated using direct kinematics equations to obtain the network with best result.     

Bayesian sparse solutions to linear inverse problems with non-stationary noise with Student-t priors

Bayesian approach has become a commonly used method for inverse problems arising in signal and image processing. One of the main advantages of the Bayesian approach is the possibility to propose unsupervised methods where the likelihood and prior model parameters can be estimated jointly with the main unknowns. In this paper, we propose to consider linear inverse problems in which the noise may be non-stationary and where we are looking for a sparse solution. To consider both of these requirements, we propose to use Student-t prior model both for the noise of the forward model and the unknown signal or image. The main interest of the Student-t prior model is its Infinite Gaussian Scale Mixture (IGSM) property. Using the resulted hierarchical prior models we obtain a joint posterior probability distribution of the unknowns of interest (input signal or image) and their associated hidden variables. To be able to propose practical methods, we use either a Joint Maximum A Posteriori (JMAP) estimator or an appropriate Variational Bayesian Approximation (VBA) technique to compute the Posterior Mean (PM) values. The proposed method is applied in many inverse problems such as deconvolution, image restoration and computed tomography. In this paper, we show only some results in signal deconvolution and in periodic components estimation of some biological signals related to circadian clock dynamics for cancer studies.     

Efficient solution of nonlinear,underdetermined inverse problems with a generalized PDE model

Several parameter estimation problems (or “inverse” problems) such as those that occur in hydrology and geophysics are solved using partial differential equation (PDE)-based models of the physical system in question. Likewise, these problems are usually underdetermined due to the lack of enough data to constrain a unique solution. In this paper, we present a framework for the solution of underdetermined inverse problems using COMSOL Multiphysics (formerly FEMLAB) that is applicable to a broad range of physical systems governed by PDEs. We present a general adjoint state formulation which may be used in this framework and allows for faster calculation of sensitivity matrices in a variety of commonly encountered underdetermined problems. The aim of this approach is to provide a platform for the solution of inverse problems that is efficient, flexible, and not restricted to one particular scientific application.We present an example application of this framework on a synthetic underdetermined inverse problem in aquifer characterization, and present numerical results on the accuracy and efficiency of this method. Our results indicate that our COMSOL-based routines provide an accurate, flexible, and scalable method for the solution of PDE-based inverse problems.     

A Polynomial Approach to Bias Aware Fixed-Lag Smoothing Problem

In the present technical note, a solution to the problem of fixed-lag smoothing of SISO systems in presence of a dynamical bias is presented in a polynomial framework. The bias aware smoothing problem is solved in three steps, namely, the design of the general structure of the smoother, the estimation of the dynamical bias by means of a deconvolution technique and, then, the combination of the previous results to obtain the bias aware fixed-lag smoother. Applied to an example, this approach shows its efficiency.      

Video super-resolution with fast deconvolution

Super-resolution problem is posed as an inverse deconvolution problem. Fast non-iterative super-resolution algorithm based on this approach is suggested. Different super-resolution problem statements for the cases of exactly and inexactly known transform operator were considered.     

Finding edges in noisy scenes

Edge detection in the presence of noise is a well-known problem. This paper examines an applications-motivated approach for solving the problem using novel techniques and presents a method developed by the authors that performs well on a large class of targets. ROC curves are used to compare this method with other well-known edge detection operators, with favorable results. A theoretical argument is presented that favors LMMSE filtering over median filtering in extremely noisy scenes. Simulated results of the research are presented.     

An efficient deconvolution algorithm for estimating oxygen consumption during muscle activities

The reconstruction of an unknown input function from noisy measurements in a biological system is an ill-posed inverse problem. Any computational algorithm for its solution must use some kind of regularization technique to neutralize the disastrous effects of amplified noise components on the computed solution. In this paper, following a hierarchical Bayesian statistical inversion approach, we seek estimates for the input function and regularization parameter (hyperparameter) that maximize the posterior probability density function. We solve the maximization problem simultaneously for all unknowns, hyperparameter included, by a suitably chosen quasi-Newton method. The optimization approach is compared to the sampling-based Bayesian approach. We demonstrate the efficiency and robustness of the deconvolution algorithm by applying it to reconstructing the time courses of mitochondrial oxygen consumption during muscle state transitions (e.g., from resting state to contraction and recovery), from the simulated noisy output of oxygen concentration dynamics on the muscle surface. The model of oxygen transport and metabolism in skeletal muscle assumes an in vitro cylindrical structure of the muscle in which the oxygen from the surrounding oxygenated solution diffuses into the muscle and is then consumed by the muscle mitochondria. The algorithm can be applied to other deconvolution problems by suitably replacing the forward model of the system.     

Synthetic aperture radar imaging with fractional Fourier transform and channel equalization

This paper investigates the Range-Doppler Algorithm based on the Fractional Fourier Transform (RDA-FrFT) to obtain High-Resolution (HR) images for targets in Synthetic Aperture Radar (SAR) imaging. A mathematical framework for the RDA-FrFT is developed in this paper with closed-form expressions for the range and azimuth compression. The channel effect is considered in this paper for the first time with three inverse techniques to reduce this effect; inverse filter deconvolution, Linear Minimum Mean Square Error (LMMSE) deconvolution, and regularized deconvolution. The performance of the RDA-FrFT is compared with the classical RDA, which is based on the Fourier Transform (FT). Simulation results reveal that the RDA-FrFT offers better focusing capabilities and greater side-lobe reduction ratios. The reflectivity profile obtained with the RDA-FrFT demonstrates a superior performance to the classical RDA. Results show also that the RDA-FrFT gives low Peak Side-Lobe (PSL) and Integrated Side-Lobe (ISL) levels after range and azimuth compression for the detected targets. Finally, the results reveal that the proposed regularized deconvolution technique enhances the performance of the RDA-FrFT significantly if the channel effect is considered.     

基于SOS技术的多项式非线性系统鲁棒控制综合

针对一类具有多项式向量场的仿射不确定非线性系统,借助多项式平方和(Sum of Squares, SOS)技术,研究其状态反馈鲁棒控制综合问题。给出了该类系统鲁棒镇定控制、以及带有保性能和H性能目标的优化控制问题的充分可解性条件。所给出的条件均被描述为由状态依赖线性矩阵不等式(LMI)组成的SOS规划,可由SOS技术直接求解。此外,通过引入附加变量给出了描述多项式矩阵的逆以及有理式矩阵的方法。最后,通过数值仿真验证了方法的有效性     

Robust Speech Dereverberation Using Multichannel Blind Deconvolution With Spectral Subtraction

A robust dereverberation method is presented for speech enhancement in a situation requiring adaptation where a speaker shifts his/her head under reverberant conditions causing the impulse responses to change frequently. We combine correlation-based blind deconvolution with modified spectral subtraction to improve the quality of inverse-filtered speech degraded by the estimation error of inverse filters obtained in practice. Our method computes inverse filters by using the correlation matrix between input signals that can be observed without measuring room impulse responses. Inverse filtering reduces early reflection, which has most of the power of the reverberation, and then, spectral subtraction suppresses the tail of the inverse-filtered reverberation. The performance of our method in adaptation is demonstrated by experiments using measured room impulse responses. The subjective results indicated that this method provides superior speech quality to each of the individual methods: blind deconvolution and spectral subtraction.     

Evolutionary approaches to signal decomposition in an application service management system

The increased demand for autonomous control in enterprise information systems has generated interest on efficient global search methods for multivariate datasets in order to search for original elements in time-series patterns, and build causal models of systems interactions, utilization dependencies, and performance characteristics. In this context, activity signals deconvolution is a necessary step to achieve effective adaptive control in Application Service Management. The paper investigates the potential of population-based metaheuristic algorithms, particularly variants of particle swarm, genetic algorithms and differential evolution methods, for activity signals deconvolution when the application performance model is unknown a priori. In our approach, the Application Service Management System is treated as a black- or grey-box, and the activity signals deconvolution is formulated as a search problem, decomposing time-series that outline relations between action signals and utilization-execution time of resources. Experiments are conducted using a queue-based computing system model as a test-bed under different load conditions and search configurations. Special attention was put on high-dimensional scenarios, testing effectiveness for large-scale multivariate data analyses that can obtain a near-optimal signal decomposition solution in a short time. The experimental results reveal benefits, qualities and drawbacks of the various metaheuristic strategies selected for a given signal deconvolution problem, and confirm the potential of evolutionary-type search to effectively explore the search space even in high-dimensional cases. The approach and the algorithms investigated can be useful in support of human administrators, or in enhancing the effectiveness of feature extraction schemes that feed decision blocks of autonomous controllers.     

Tsp-based scheduling in a batch-wise hybrid flow-shop

In the past few years, flexible production systems have allowed an extensive exploitation of new technologies, but have also led to new difficulties in production planning management science. The model presented in this paper extends the traditional HFS (hybrid flow-shop) scheduling problem to the case in which jobs are due to follow strict precedence constraints and batch assignment constraints and the parallel machines at a stage are served by a bottleneck machine. A variant of the well-known TSP problem is used to develop an efficient heuristic solution for the problem. The effectiveness of the proposed approach is validated through a comparison with different heuristics traditionally used in HFS scheduling problems. Furthermore, a simple insertion heuristic based on the TSP model of the problem is tested. Finally, a MIP-based approach is also explored to provide the optimum solutions within much larger times for comparison.     

A Bayesian solution and its approximations to out-of-sequence measurement problems

Target tracking using delayed, out-of-sequence measurements is a problem of growing importance due to an increased reliance on networked sensors interconnected via complex communication network architectures. In such systems, it is often the case that measurements are received out-of-time-order at the fusion center. This paper presents a Bayesian solution to this problem and provides approximate, implementable algorithms for both cluttered and non-cluttered scenarios involving single and multiple time-delayed measurements. Such an approach leads to a solution involving the joint probability density of current and past target states.In contrast, existing solutions in the literature modify the sensor measurement equation to account for the time delay and explicitly deal with the resulting correlations that arise in the process noise and current target state. In the Bayesian solution proposed in this paper, such cross correlations are treated implicitly. Under linear Gaussian assumptions, the Bayesian solution reduces to an augmented state Kalman filter (AS-KF) for scenarios devoid of clutter and an augmented state probabilistic data association filter (AS-PDA) for scenarios involving clutter. Computationally efficient versions of AS-KF and AS-PDA are considered in this paper. Simulations are presented to evaluate the performance of these solutions.