Transcript Utilizing High-Performance Computing to Investigate

Utilizing High-Performance Computing to Investigate
Performance and Sensitivity of an Inversion Model for
Hyperspectral Remote Sensing of Shallow Coral Ecosystems
Carolina Gerardino (UPRM)
Dr. James Goodman (UPRM), Dr. Wilson Rivera (UPRM)
[email protected], [email protected], [email protected]
This work was supported in part by CenSSIS, the Center for Subsurface Sensing and Imaging Systems,
under the Engineering Research Centers Program of the National Science Foundation (Award Number ECE-9986821).
Abstract
Working with Synthetic Vector
This poster describes the implementation
of a semi-analytical inversion model within a
parallel processing framework. Preliminary
results of the implementation in a C++/OOL,
C++/MPI and the IDL/ENVI environment using a
synthetic vector are presented. The C++/OOL
implementation provides both the foundation
for
assessing
real-time
processing
capabilities as well as the computation power
necessary for addressing complex optimization
and sensitivity questions.
Forward Model
rrs  rrsdp
 Applications to simultaneously classify
water properties, bathymetry and benthic
composition
using
hyperspectral
remote
sensing was previously demonstrated using
AVIRIS imagery from Hawaii [1]. At the core
of this approach was the application of a
semi-analytical
inversion
model
for
simultaneously extracting bathymetry and
water property parameters.
 The semi-analytical inversion model employs
a
non-linear
optimization
routine
to
retrieve estimates of bathymetry and water
properties, the algorithm is based on
quasi-single-scattering theory, and was
developed utilizing Hydrolight (Sequoia
Scientific Inc.) simulations to populate
parameters of the semi-analytical model
[2].
 The
advantages
of
utilizing
high
performance computing resources to solve
hyperspectral imaging problems (CPU time
and memory capacity) has been previously
demonstrated [3,4,7].
1


  C
1  

1  exp   Du 
 kH 

cos


w
 

 
 exp    DuB 
 

1 

kH


cos w 

SA studies the effect of changes in model
assumptions (Nuisance Parameters) on a given
output (Parameters of interest)[9].
={… … …}
 output
For the SA, the objective function is
redefined in function of two types of
parameters:
Nuisance
parameters
(γ)
and
Parameters of interest(θ).
Optimization,
Inversion method
(2)
2
2
.
2
Parameters of interest
  {P, G, BP, B, H },
The semi-analytical model has been implemented
in C++ using the Message Passing Interface
(MPI) [5.
Nuisance Parameters
  {S , Y1, Y2 , Y3 , b1, b2 , D0 , D1, D0' , D1' , g0 , g1,  , }
Additionally, for solving the constrained
nonlinear optimization problem were tested
different optimization libraries:
• ConminC++ Library [6][7]
• OOL (Open Optimization Library) [8]
Sensitivity Analysis
Forward Model
  {P, G, B P, B, H },

( , )
Experimental Results
F
o
r
w
a
r
d
={0.05, 0.05, 0.01, 0.4, 1.5}

 

1 
rrs  rrsdp 1  exp    DuC 
 kH 

cos w 
 


1






 exp 
 DB 
  u
Rrs 
0.5 rrs
1  1.5 rrs


1
 kH 

cos w 

(2)
(3)
M
o
d
e
l
Rrs
Rrs  {.....}
Comparison of optimization routines with
H=1meter
θ
Error (%)
14.4
H error P
10
H error G
5
1.8 2.9
0.4
3.1
1.2 0.5
0.5
H error B
0 0 0 0
0
M
o
d
e
l
I
n
v
e
r
s
i
o
n
Inversion Model
Simlab
Has to be the same
or
approx
={…
… .…}
={…….}
o u tp u t
γ
Optimization,
Inversion method
FAST
Method
 initial ={0.05, 0.2, 0.001, 0.1, 1}
SA
H error H
CONMIN
IDL
OOL
Optimization routines
Figure 2. Error of the different optimization routine
Value Added to CenSSIS
Comparison of optimization routines for BP with
H=1meter
Error (%)
Implementing hyperspectral algorithms into
parallel computing frameworks provides both
the
foundation
for
assessing
real-time
processing
capabilities
as
well
as
the
computational power necessary for addressing
complex
optimization
and
sensitivity
questions.
2
Rrs  {.....}
15
Remote sensing is increasingly being employed
as a significant component in the evaluation
and management of coral ecosystems (visual
overview, and the quantitative abilities for
systematic
assessment
and
monitoring).
Hyperspectral
instruments
provide
much
greater spectral detail, and thus an improved
ability
to
extract
multiple
layers
of
information
from
the
spectrally
complex
environment associated with coral reefs and
other shallow costal subsurface environments.
Rˆ rs ( ,  )
 initial={0.05, 0.2, 0.001, 0.1, 1}
20
Significance
Rrs  Rˆ rs ( ,  )
err ( ,  ) 
Synthetic
Vector
0.5 rrs
Rrs 
(3)
1  1.5 rrs
Sensitivity Analysis (SA)
Has to be the
same or approx.
={0.05, 0.05, 0.01, 0.4, 1.5}
Clear
Waters

State of the Art
Inversion Model
  {P, G, BP, B, H },

Future Research
898.6
1000
500
error BP
53.1
0
IDL
OOL
0
CONMIN
Model Implementation
Optimization routines
P: Phytoplankton absorption at 440nm (m-1)
G: Gelbstoff/detritus absorption at 440nm (m-1)
BP: Absorption coefficient for particle backscattering, view angle and sea state (m-1)
B: Bottom albedo at 550nm
H: Water depth (m)
2
2
ˆ
ˆ
(
R

R
)

(
R

R
)


rs
rs
rs
rs 



405
720
obj 
0.5
800
675 ˆ

(1)
ˆ
  ( Rrs )   ( Rrs )
405

720
800
0.5
(3)
The inversion model is a function of both rrs,
subsurface remote sensing reflectance(2), and
Rrs, above surface remote sensing reflectance
(3).
Figure 3. Error of the different optimization routine
for parameter BP
Execution time Vs Number of processors
1. Goodman, J.A. (2004). Hyperspectral remote sensing of
coral reefs: deriving bathymetry, aquatic optical
properties and a benthic spectral unmixing classification
using AVIRIS data in the Hawaiian Islands. PhD
Dissertation, University of California, Davis.
2. Lee, Z.P., K. Carder, C.D. Mobley, R. Steward, and J.
Patch (1998). Hyperspectral remote sensing for shallow
waters. 1. a semi-analytical model. Applied Optics, 37,
6329-6338.
3. Lugo-Beauchamp, W., C. Carvajal-Jimenez and W. Rivera
(2004). Performance of Hyperspectral Imaging Algorithms on
IA-64. Proc. IASTED International Conference on Circuits,
Signals, and Systems, p. 327-332.
12000
Time (seconds)
A semi-analytical inversion model [2,3] is
independently applied to each pixel of a
hyperspectral image, finding the parameters
that minimize the error of the objective
function, obj (1). These parameters are:
675
References
10000
4. Hawick, K.A. and H. A. James (1997). Distributed highperformance computing for remote sensing. Proceedings of
the ACM/IEEE Conference on Supercomputing.
8000
6000
5. Snir, M., S. Otto, S. Huss-Lederman, D. Walker and J.
Dongarra (1998). MPI–The Complete Reference. Volume 1 The MPI-1 Core, 2nd edition. The MIT Press.
4000
2000
0
1
8
20
32
44
56
68
80
92 104 116 128
Number of processors
Figure 2. Parallel execution times of Kaneohe
Bay hyperspectral image with OOL.
6. NASA (1978). Conmin User’s Manual. NASA Technical
Memorandum X-62282.
7. C. Gerardino, Y. Rivera, W. Rivera, and J. A. Goodman
(2006), Parallel implementation of an inversion model for
hyperspectral remote sensing. 49th IEEE International
Midwest Symposium on Circuits and Systems(submitted).
8. http://ool.sourceforge.net/ OOL (Open Optimization
Library)
9. Saltelli, A., Tarantola S. Campolongo F. and Rato
(2004), “Sensitivity Analysis in Practice A Guide
Assessing Scientific Models ”. John Wiley & Sons.
M.
to