scholarly journals Alternating Projections Filtering Algorithm to Track Moving Objects

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Youssef Qranfal
Keyword(s):  
Inverse Problem ◽  
Moving Objects ◽  
Aerospace Engineering ◽  
Time Varying ◽  
Alternating Projections ◽  
Filtering Algorithm ◽  
Engineering Control ◽  
Ill Posed ◽  
Iterative Filtering ◽  
Quantities Of Interest

An interest is often present in knowing evolving variables that are not directly observable; this is the case in aerospace, engineering control, medical imaging, or data assimilation. What is at hand, though, are time-varying measured data, a model connecting them to variables of interest, and a model of how to evolve the variables over time. However, both models are only approximation and the observed data are tainted with noise. This is an ill-posed inverse problem. Methods, such as Kalman filter (KF), have been devised to extract the time-varying quantities of interest. These methods applied to this inverse problem, nonetheless, are slow, computation wise, since they require large matrices multiplications and even matrix inversion. Furthermore, these methods are not usually suitable to impose some constraints. This article introduces a new iterative filtering algorithm based on alternating projections. Experiments were run with simulated moving projectiles and were compared with results using KF. The new optimization algorithm proves to be slightly more accurate than KF, but, more to the point, it is much faster in terms of CPU time.

scholarly journals Bayesian Reconstruction through Adaptive Image Notion

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 21
Author(s):  
Fabrizia Guglielmetti ◽  
Eric Villard ◽  
Ed Fomalont
Keyword(s):  
Inverse Problem ◽  
Image Plane ◽  
Source Distribution ◽  
Bayesian Probability ◽  
Model Parameters ◽  
Uncertain Information ◽  
Source Detection ◽  
Component Mixture ◽  
Ill Posed ◽  
Image Planes

A stable and unique solution to the ill-posed inverse problem in radio synthesis image analysis is sought employing Bayesian probability theory combined with a probabilistic two-component mixture model. The solution of the ill-posed inverse problem is given by inferring the values of model parameters defined to describe completely the physical system arised by the data. The analysed data are calibrated visibilities, Fourier transformed from the ( u , v ) to image planes. Adaptive splines are explored to model the cumbersome background model corrupted by the largely varying dirty beam in the image plane. The de-convolution process of the dirty image from the dirty beam is tackled in probability space. Probability maps in source detection at several resolution values quantify the acquired knowledge on the celestial source distribution from a given state of information. The information available are data constrains, prior knowledge and uncertain information. The novel algorithm has the aim to provide an alternative imaging task for the use of the Atacama Large Millimeter/Submillimeter Array (ALMA) in support of the widely used Common Astronomy Software Applications (CASA) enhancing the capabilities in source detection.

Advances in Tracking and Recognition of Human Motion

2011 ◽  
pp. 65-71
Author(s):  
Niki Aifanti ◽  
Angel D. Sappa ◽  
Nikos Grammalidis ◽  
Sotiris Grammalidis Malassiotis
Keyword(s):  
Moving Objects ◽  
Research Area ◽  
Initial Position ◽  
Human Motion ◽  
Target Person ◽  
Motion Constraints ◽  
Simplifying Assumptions ◽  
Ill Posed ◽  
Important Research Area ◽  
Tracking And Recognition

Tracking and recognition of human motion has become an important research area in computer vision. In real world conditions it constitutes a complicated problem, considering cluttered backgrounds, gross illumination variations, occlusions, self-occlusions, different clothing and multiple moving objects. These ill-posed problems are usually tackled by making simplifying assumptions regarding the scene or by imposing constraints on the motion. Constraints such as that the contrast between the moving people and the background should be high and that everything in the scene should be static except for the target person are quite often introduced in order to achieve accurate segmentation. Moreover, the motion of the target person is often confined to simple movements with limited occlusions. In addition, assumptions such as known initial position and posture of the person are usually imposed in tracking processes.

scholarly journals Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 228
Author(s):  
Rasoul Shafipour ◽  
Gonzalo Mateos
Keyword(s):  
Inverse Problem ◽  
Covariance Matrix ◽  
A Priori ◽  
Dynamic Network ◽  
Streaming Data ◽  
Optimal Time ◽  
Time Varying ◽  
Graph Learning ◽  
Topology Inference ◽  
Diffusion Dynamics

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

ON THE WAY TOWARDS INCREASING THE PREDICTIVE POWER OF THE NUCLEAR MEAN FIELD THEORIES: EVALUATION OF TWO-BODY MATRIX ELEMENTS

2012 ◽  
Vol 21 (05) ◽  
pp. 1250037
Author(s):  
HERVÉ MOLIQUE ◽  
JERZY DUDEK
Keyword(s):  
Inverse Problem ◽  
Predictive Power ◽  
Mean Field ◽  
Field Theories ◽  
Matrix Elements ◽  
The Matrix ◽  
Ill Posed ◽  
Technical Issues ◽  
Numerical Precision ◽  
Mean Field Theories

In this paper we collect a number of technical issues that arise when constructing the matrix representation of the most general nuclear mean field Hamiltonian within which "all terms allowed by general symmetries are considered not only in principle but also in practice". Such a general posing of the problem is necessary when investigating the predictive power of the mean field theories by means of the well-posed inverse problem. [J. Dudek et al., Int. J. Mod. Phys. E21 (2012) 1250053]. To our knowledge quite often ill-posed mean field inverse problems arise in practical realizations what makes reliable extrapolations into the unknown areas of nuclei impossible. The conceptual and technical issues related to the inverse problem have been discussed in the above-mentioned topic whereas here we focus on "how to calculate the matrix elements, fast and with high numerical precision when solving the inverse problem" [For space-limitation reasons we illustrate the principal techniques on the example of the central interactions].

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