Sensitivity Analysis (SA)

SA studies the effect of changes in model assumptions (Nuisance Parameters) on a given output (Parameters of interest)[9].

For the SA, the objective function is redefined in function of two types of parameters: Nuisance parameters (γ) and Parameters of interest(θ).

Sensitivity Analysis

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:

P: Phytoplankton absorption at 440nm (m-1)G: Gelbstoff/detritus absorption at 440nm (m-1)BP: Absorption coefficient for particle back- scattering, view angle and sea state (m-1)B: Bottom albedo at 550nmH: Water depth (m)

The inversion model is a function of both rrs, subsurface remote sensing reflectance(2), and Rrs, above surface remote sensing reflectance (3).

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.

4. Hawick, K.A. and H. A. James (1997).  Distributed high-performance computing for remote sensing. Proceedings of the ACM/IEEE Conference on Supercomputing.

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.

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 M. (2004), “Sensitivity Analysis in Practice A Guide to Assessing Scientific Models ”. John Wiley & Sons.

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].

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.

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.

Figure 2. Parallel execution times of Kaneohe Bay hyperspectral image with OOL.

Figure 2. Error of the different optimization routine

Carolina Gerardino (UPRM)Dr. James Goodman (UPRM), Dr. Wilson Rivera (UPRM)

carolina.gerardino@ece.uprm.edu, jgoodman@uprm.edu, wrivera@ece.uprm.edu

Utilizing High-Performance Computing to Investigate Performance and Sensitivity of an Inversion Model for

Hyperspectral Remote Sensing of Shallow Coral Ecosystems

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).

Execution time Vs Number of processors

0

2000

4000

6000

8000

10000

12000

1 8 20 32 44 56 68 80 92 104 116 128

Number of processors

Tim

e (s

econ

ds)

The semi-analytical model has been implemented in C++ using the Message Passing Interface (MPI) [5.

Additionally, for solving the constrained nonlinear optimization problem were tested different optimization libraries:• ConminC++ Library [6][7]• OOL (Open Optimization Library) [8]

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.

Abstract

State of the Art

Significance

Model Implementation

Working with Synthetic Vector

(1)5.0800

720

675

405

5.0800

720

2675

405

2

)ˆ()ˆ(

)ˆ()ˆ(

rsrs

rsrsrsrs

RR

RRRRobj (3)

Experimental Results

Comparison of optimization routines with H=1meter

14.4

1.23.1

0.5 01.8 02.9

00.50.4 00

5

10

15

20

CONMIN IDL OOLOptimization routines

Err

or

(%)

H error P

H error G

H error B

H error H

Comparison of optimization routines for BP with H=1meter

898.6

53.1 00

500

1000

CONMIN IDL OOL

Optimization routines

Erro

r (%

)

error BP

Figure 3. Error of the different optimization routine for parameter BP

References

Value Added to CenSSIS

Future Research

},,,,,{ HBBPGP

Parameters of interest

},,,,,,,,,,,,,{ 10'1

'01021321 ggDDDDbbYYYS

Nuisance Parameters

{.....}rsR

},,,,,{ HBBPGP

rs

rsrs r

rR

5.11

5.0

kHDrr

w

Cu

dprsrs cos

1exp1

kHD

w

Bu

cos

1exp

1

={0.05, 0.05, 0.01, 0.4, 1.5}

Optimization,Inversion method

Clear Waters

output

Has to be the same or approx.

Synthetic Vector

Forward Model

initial

Inversion Model

={0.05, 0.2, 0.001, 0.1, 1}(3)

(2)

={… … …}

={…….}

Rrs

{.....}rsR

={0.05, 0.05, 0.01, 0.4, 1.5}

},,,,,{ HBBPGP

rs

rsrs r

rR

5.11

5.0

kHDrr

w

Cu

dprsrs cos

1exp1

kHD

w

Bu

cos

1exp

1

Forward Model

(3)

(2)

F o Mr ow da er ld

Optimization,Inversion method

output

Has to be the same

or approx.

initial

Inversion Model

={0.05, 0.2, 0.001, 0.1, 1}

I M n o v d e e r l s i o n

Simlab

FASTMethod

={… … …}

),(

γθ

SA