113 research outputs found
Sampling systems matched to input processes and image classes
This dissertation investigates sampling and reconstruction of wide sense stationary (WSS) random processes from their sample random variables . In this context, two types of sampling systems are studied, namely, interpolation and approximation sampling systems. We aim to determine the properties of the filters in these systems that minimize the mean squared error between the input process and the process reconstructed from its samples. More specifically, for the interpolation sampling system we seek and obtain a closed form expression for an interpolation filter that is optimal in this sense. Likewise, for the approximation sampling system we derive a closed form expression for an optimal reconstruction filter given the statistics of the input process and the antialiasing filter. Using these expressions we show that Meyer-type scaling functions and wavelets arise naturally in the context of subsampled bandlimited processes. We also derive closed form expressions for the mean squared error incurred by both the sampling systems. Using the expression for mean squared error we show that for an approximation sampling system, minimum mean squared error is obtained when the antialiasing filter and the reconstruction filter are spectral factors of an ideal brickwall-type filter. Similar results are derived for the discrete-time equivalents of these sampling systems. Finally, we give examples of interpolation and approximation sampling filters and compare their performance with that of some standard filters. The implementation of these systems is based on a novel framework called the perfect reconstruction circular convolution (PRCC) filter bank framework. The results obtained for the one dimensional case are extended to the multidimensional case. Sampling a multidimensional random field or image class has a greater degree of freedom and the sampling lattice can be defined by a nonsingular matrix D. The aim is to find optimal filters in multidimensional sampling systems to reconstruct the input image class from its samples on a lattice defined by D. Closed form expressions for filters in multidimensional interpolation and approximation sampling systems are obtained as are expressions for the mean squared error incurred by each system. For the approximation sampling system it is proved that the antialiasing and reconstruction filters that minimize the mean squared error are spectral factors of an ideal brickwall-type filter whose support depends on the sampling matrix D. Finally. we give examples of filters in the interpolation and approximation sampling systems for an image class derived from a LANDSAT image and a quincunx sampling lattice. The performance of these filters is compared with that of some standard filters in the presence of a quantizer
A Dynamic Boundary Guarding Problem with Translating Targets
We introduce a problem in which a service vehicle seeks to guard a deadline
(boundary) from dynamically arriving mobile targets. The environment is a
rectangle and the deadline is one of its edges. Targets arrive continuously
over time on the edge opposite the deadline, and move towards the deadline at a
fixed speed. The goal for the vehicle is to maximize the fraction of targets
that are captured before reaching the deadline. We consider two cases; when the
service vehicle is faster than the targets, and; when the service vehicle is
slower than the targets. In the first case we develop a novel vehicle policy
based on computing longest paths in a directed acyclic graph. We give a lower
bound on the capture fraction of the policy and show that the policy is optimal
when the distance between the target arrival edge and deadline becomes very
large. We present numerical results which suggest near optimal performance away
from this limiting regime. In the second case, when the targets are slower than
the vehicle, we propose a policy based on servicing fractions of the
translational minimum Hamiltonian path. In the limit of low target speed and
high arrival rate, the capture fraction of this policy is within a small
constant factor of the optimal.Comment: Extended version of paper for the joint 48th IEEE Conference on
Decision and Control and 28th Chinese Control Conferenc
Hide-and-Seek with Directional Sensing
We consider a game played between a hider, who hides a static object in one
of several possible positions in a bounded planar region, and a searcher, who
wishes to reach the object by querying sensors placed in the plane. The
searcher is a mobile agent, and whenever it physically visits a sensor, the
sensor returns a random direction, corresponding to a half-plane in which the
hidden object is located. We first present a novel search heuristic and
characterize bounds on the expected distance covered before reaching the
object. Next, we model this game as a large-dimensional zero-sum dynamic game
and we apply a recently introduced randomized sampling technique that provides
a probabilistic level of security to the hider. We observe that, when the
randomized sampling approach is only allowed to select a very small number of
samples, the cost of the heuristic is comparable to the security level provided
by the randomized procedure. However, as we allow the number of samples to
increase, the randomized procedure provides a higher probabilistic security
level.Comment: A short version of this paper (without proofs) will be presented at
the 18th IFAC World Congress (IFAC 2011), Milan (Italy), August 28-September
2, 201
FlipDyn with Control: Resource Takeover Games with Dynamics
We present the FlipDyn, a dynamic game in which two opponents (a defender and
an adversary) choose strategies to optimally takeover a resource that involves
a dynamical system. At any time instant, each player can take over the resource
and thereby control the dynamical system after incurring a state-dependent and
a control-dependent costs. The resulting model becomes a hybrid dynamical
system where the discrete state (FlipDyn state) determines which player is in
control of the resource. Our objective is to compute the Nash equilibria of
this dynamic zero-sum game. Our contributions are four-fold. First, for any
non-negative costs, we present analytical expressions for the saddle-point
value of the FlipDyn game, along with the corresponding Nash equilibrium (NE)
takeover strategies. Second, for continuous state, linear dynamical systems
with quadratic costs, we establish sufficient conditions under which the game
admits a NE in the space of linear state-feedback policies. Third, for scalar
dynamical systems with quadratic costs, we derive the NE takeover strategies
and saddle-point values independent of the continuous state of the dynamical
system. Fourth and finally, for higher dimensional linear dynamical systems
with quadratic costs, we derive approximate NE takeover strategies and control
policies which enable the computation of bounds on the value functions of the
game in each takeover state. We illustrate our findings through a numerical
study involving the control of a linear dynamical system in the presence of an
adversary.Comment: 17 Pages, 2 figures. Under review at IEEE TA
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