Closely Spaced Object Resolution Using a Quantum Annealing Model

37 Pages·2014·0.57 MB·English

Closely Spaced Object Resolution Using a
Quantum Annealing Model
J.J. Tran1,2 R.F. Lucas1 K.J. Scully2 D.L. Semmen2
1InformationSciencesInstitute
UniversityofSouthernCalifornia
2SystemsPerformance,EstimationandAlgorithmsDepartment
TheAerospaceCorporation
IS&T/SPIE Electronic Imaging 2014
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 1/34
Outline
1 Motivation
2 Background
Problem Description
Ising Model
Graph Partitioning Example
3 Our Approach to the CSO Problem
Estimation Model
Hamiltonian in Ising Form
Analysis
4 Summary
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 2/34
Motivation
Given an image of a two-dimensional focal plane, we are interested in
determining:
How many unique objects are present in the focal plane?
What are their locations and amplitudes?
These questions are integral parts of automated target recognition and
target tracking.
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 3/34
Motivation
Given an image of a two-dimensional focal plane, we are interested in
determining:
How many unique objects are present in the focal plane?
What are their locations and amplitudes?
These questions are integral parts of automated target recognition and
target tracking.
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 3/34
Motivation
Research Interest
Generally speaking, we have seen several decades of research
devoted to the problem of closely spaced objects (CSO) and the focus
has been on:
Better sensors
Adopting heuristics to improve local optimal solutions
To our knowledge, not much research has been devoted to:
Complexity analysis of the CSO algorithms
Tackling one of the most difficult issues with CSO algorithms: the
underlying performance barrier when considering a large-scale
scenarios with many CSO’s
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 4/34
Motivation
Research Interest
Generally speaking, we have seen several decades of research
devoted to the problem of closely spaced objects (CSO) and the focus
has been on:
Better sensors
Adopting heuristics to improve local optimal solutions
To our knowledge, not much research has been devoted to:
Complexity analysis of the CSO algorithms
Tackling one of the most difficult issues with CSO algorithms: the
underlying performance barrier when considering a large-scale
scenarios with many CSO’s
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 4/34
Motivation
The CSO problem is a Combinatoric Problem
This presentation will:
Examine the complexity of the traditional approach to resolving
CSO’s
Look at how an NP-Hard problem can be solved if it can be
mapped to the Ising model
MapthetraditionalapproachtoresolvingCSO’stotheIsingmodel
which can (in theory) be programmed on a Quantum Annealing
optimization platform
We note that our presentation addresses only the estimation part of
the CSO-resolution algorithm. This is the computationally-intensive
prelude to a simple statistical classification based on the Bayesian
information criterion (BIC) or the Akaike information criterion (AIC).
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 5/34
Motivation
The CSO problem is a Combinatoric Problem
This presentation will:
Examine the complexity of the traditional approach to resolving
CSO’s
Look at how an NP-Hard problem can be solved if it can be
mapped to the Ising model
MapthetraditionalapproachtoresolvingCSO’stotheIsingmodel
which can (in theory) be programmed on a Quantum Annealing
optimization platform
We note that our presentation addresses only the estimation part of
the CSO-resolution algorithm. This is the computationally-intensive
prelude to a simple statistical classification based on the Bayesian
information criterion (BIC) or the Akaike information criterion (AIC).
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 5/34
Background ProblemDescription
Outline
1 Motivation
2 Background
Problem Description
Ising Model
Graph Partitioning Example
3 Our Approach to the CSO Problem
Estimation Model
Hamiltonian in Ising Form
Analysis
4 Summary
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 6/34
Background ProblemDescription
2D Focal Plane Image
This simulated focal plane array image is a simple example of the
problem:
Two targets spaced 1.25 pixels apart, each with an SNR of 10
Energy-on-detector (EOD) is 0.6
Gaussian noise added (µ = 0 and σ = 1)
Tran,Lucas,Scully,andSemmen CSOwithQuantumAnnealing IS&T/SPIE2014 7/34