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Reconstruction Problem (reconstruction + problem)
Selected AbstractsDesign of an FIR filter for the displacement reconstruction using measured acceleration in low-frequency dominant structuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Hae Sung Lee Abstract This paper presents a new class of displacement reconstruction scheme using only acceleration measured from a structure. For a given set of acceleration data, the reconstruction problem is formulated as a boundary value problem in which the acceleration is approximated by the second-order central finite difference of displacement. The displacement is reconstructed by minimizing the least-squared errors between measured and approximated acceleration within a finite time interval. An overlapping time window is introduced to improve the accuracy of the reconstructed displacement. The displacement reconstruction problem becomes ill-posed because the boundary conditions at both ends of each time window are not known a priori. Furthermore, random noise in measured acceleration causes physically inadmissible errors in the reconstructed displacement. A Tikhonov regularization scheme is adopted to alleviate the ill-posedness. It is shown that the proposed method is equivalent to an FIR filter designed in the time domain. The fundamental characteristics of the proposed method are presented in the frequency domain using the transfer function and the accuracy function. The validity of the proposed method is demonstrated by a numerical example, a laboratory experiment and a field test. Copyright © 2009 John Wiley & Sons, Ltd. [source] Signal reconstruction in the presence of finite-rate measurements: finite-horizon control applicationsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2010Sridevi V. Sarma Abstract In this paper, we study finite-length signal reconstruction over a finite-rate noiseless channel. We allow the class of signals to belong to a bounded ellipsoid and derive a universal lower bound on a worst-case reconstruction error. We then compute upper bounds on the error that arise from different coding schemes and under different causality assumptions. When the encoder and decoder are noncausal, we derive an upper bound that either achieves the universal lower bound or is comparable to it. When the decoder and encoder are both causal operators, we show that within a very broad class of causal coding schemes, memoryless coding prevails as optimal, imposing a hard limitation on reconstruction. Finally, we map our general reconstruction problem into two important control problems in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a finite-rate noiseless channel. The first problem is to minimize a finite-horizon weighted tracking error between the remote system output and a reference command. The second problem is to navigate the state of the remote system from a nonzero initial condition to as close to the origin as possible in finite-time. Our analysis enables us to quantify the tradeoff between time horizon and performance accuracy, which is not well studied in the area of control with limited information as most works address infinite-horizon control objectives (e.g. stability, disturbance rejection). Copyright © 2009 John Wiley & Sons, Ltd. [source] Generalized MRI reconstruction including elastic physiological motion and coil sensitivity encodingMAGNETIC RESONANCE IN MEDICINE, Issue 6 2008Freddy Odille Abstract This article describes a general framework for multiple coil MRI reconstruction in the presence of elastic physiological motion. On the assumption that motion is known or can be predicted, it is shown that the reconstruction problem is equivalent to solving an integral equation,known in the literature as a Fredholm equation of the first kind,with a generalized kernel comprising Fourier and coil sensitivity encoding, modified by physiological motion information. Numerical solutions are found using an iterative linear system solver. The different steps in the numerical resolution are discussed, in particular it is shown how over-determination can be used to improve the conditioning of the generalized encoding operator. Practical implementation requires prior knowledge of displacement fields, so a model of patient motion is described which allows elastic displacements to be predicted from various input signals (e.g., respiratory belts, ECG, navigator echoes), after a free-breathing calibration scan. Practical implementation was demonstrated with a moving phantom setup and in two free-breathing healthy subjects, with images from the thoracic-abdominal region. Results show that the method effectively suppresses the motion blurring/ghosting artifacts, and that scan repetitions can be used as a source of over-determination to improve the reconstruction. Magn Reson Med, 2008. © 2008 Wiley-Liss, Inc. [source] Correctness of a particular solution of inverse problem in rocking curve imagingPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 8 2009Isabella Huber Abstract Local lattice misorientations on crystalline substrates can be visualized by rocking curve imaging. Local deviations from Bragg peak positions are extracted from a series of digital topographs recorded by a CCD detector under different azimuths. Bragg peaks from surface regions such as crystallites with a larger local misorientation overlap on the detector, which requires a back-projection method in order to reconstruct the misorientation components on the sample surface from the measured angular position on the detector planes. From mathematical point of view, the reconstruction problem is an inverse problem. In this paper, we formulate the forward and back-projection problems and we prove the correctness of a particular solution. The usability of the method is demonstrated on a phantom data set. [source] FAULT DETECTION, ISOLATION AND RECONSTRUCTION FOR DESCRIPTOR SYSTEMSASIAN JOURNAL OF CONTROL, Issue 4 2005Tae-Kyeong Yeu ABSTRACT In this paper, we consider fault detection, isolation and reconstruction problem for descriptor systems with actuator faults and sensor faults, respectively. When actuator faults exist in the system, the fault detection and isolation (FDI) problem is solved through an unknown input observer regarding remaining faults excluded a specified fault as unknown inputs. Whereas, in existing sensor faults, the fault detection is only achieved by the unknown input observer and residual signals. Since the derivative signal of sensor fault is generated in the error dynamics between the actual system and the derived observer. The main objective of this work attempts the reconstruction of the faults. The reconstruction can be achieved by sliding mode observer including feedforward injection map and compensation signal. Finally, the isolation problem of sensor faults is solved by reconstructing all of the faults. [source] Incomplete oblique projections method for solving regularized least-squares problems in image reconstructionINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 4 2008H. D. Scolnik Abstract In this paper we improve on the incomplete oblique projections (IOP) method introduced previously by the authors for solving inconsistent linear systems, when applied to image reconstruction problems. That method uses IOP onto the set of solutions of the augmented system Ax,r=b, and converges to a weighted least-squares solution of the system Ax=b. In image reconstruction problems, systems are usually inconsistent and very often rank-deficient because of the underlying discretized model. Here we have considered a regularized least-squares objective function that can be used in many ways such as incorporating blobs or nearest-neighbor interactions among adjacent pixels, aiming at smoothing the image. Thus, the oblique incomplete projections algorithm has been modified for solving this regularized model. The theoretical properties of the new algorithm are analyzed and numerical experiments are presented showing that the new approach improves the quality of the reconstructed images. [source] | ||||||||||