Ocean Color Inversion by Particle Swarm ... - Semantic Scholar

Ocean Color Inversion by Particle Swarm Optimization Wayne H. Slade(1), Habtom Ressom(1), Mohamad T. Musavi(1), Richard L. Miller(2) (1) Deptartment of Electrical and Computer Engineering, University of Maine, 5708 Barrows Hall, Orono, ME 04469, USA (2) Earth Science Applications Directorate, NASA Stennis Space Center, MS 39529, USA

Overview 

Application of PSO to remote sensing problem

• • •

      

Processing of imagery requires fast algorithms Spectral matching techniques are usually not well-behaved problems (local optima) GA and PSO are good at determining global optima, but GA are too slow

Motivations for Ocean Color Inversion Ocean Color 101 Ocean Color Forward and Inverse Models Spectral Matching Approach Particle Swarm Optimization PSO-Based Inversion Results Conclusions

21 June 2004

Ocean Color Inversion by Particle Swarm Optimization

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1

Overview 

Application of PSO to remote sensing domain

• • •

      

Processing of imagery requires fast algorithms Spectral matching techniques are usually not well-behaved problems (local optima) GA and PSO are good at determining global optima, but GA are too slow

Motivations for Ocean Color Inversion Ocean Color 101 Ocean Color Forward and Inverse Models Spectral Matching Approach Particle Swarm Optimization PSO-Based Inversion Results Conclusions

21 June 2004

Ocean Color Inversion by Particle Swarm Optimization

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Overview       

Motivations for Ocean Color Inversion Ocean Color 101 Ocean Color Forward and Inverse Models Spectral Matching Approach Particle Swarm Optimization PSO-Based Inversion Results Conclusions

21 June 2004

Ocean Color Inversion by Particle Swarm Optimization

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Motivation for Ocean Color Inversion 

Assessment of ocean and coastal biogeochemistry from the color of ocean water

• • •



Remote sensing is the only feasible means for long time series, repeat, high resolution observation of biogeochemistry

• • •

  

Absorption and scatter by water constituents Biology – community structure, health Geology – sediment dynamics, carbon cycle

Long term – daily satellite ocean color since 1997 Repeat – Typical local area revisit time ~1 day by satellite High resolution – ~1 km satellite, ~1 m airborne

Past focus has been open ocean, current challenge is the coastal zone Coastal region is disproportionately important – human impact, ecological monitoring, climate models, carbon cycle We need fast, robust, and accurate algorithms for inversion of ocean color data Ocean Color Inversion by Particle Swarm Optimization

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Ocean Color 101 



Absorption and scatter of light by water constituents influences the apparent color of water Rrs(λ) is a convenient way of expressing the color of the water surface (spectral reflectance)

• • •

Rrs(λ) = Lw(λ) / Ed(λ), λ is wavelength of light Retrieval from space is possible, at the mercy of atmospheric correction Ocean color signal is ~10% of signal received at satellite

31°

Rrs(λ) [sr-1] 30°

29°

28° -94°

-93°

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-92°

-91°

-90°

-89°

-88°

400

450

500

550 600 650 Wavelength, λ [nm]

Ocean Color Inversion by Particle Swarm Optimization

700

750

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Ocean Color 101 (2) 

Typical models for ocean optics include

• • • • •

Phytoplankton – particles, strongly absorbing pigments Non-algal particles – sediment, detritus, absorbs and scatters Dissolved matter – typically organics, some terrestrial, some from phytoplankton, negligible scatter, sometimes strong absorption Usually interested in spectral (optical) absorption ([a m-1]) and backscatter (bb [m-1]) of various constituents Total absorption, total backscatter are the sum of the individual constituents: a( )  a( w) ( )  a( ) ( )  a( nap) ( )  a( cdm) ( ) bb ( )  bb ( w) ( )  bb ( ) ( )  bb ( nap) ( )



Spectral models for optical properties of various water constituents must be assumed

•



Decades of research have provided reasonable models for these constituents…

Once we determine the optically active constituents, we can use spectral matching (optimization) to figure out their relative concentrations

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Ocean Color Forward and Inverse Models

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

S

Inverse Model is the task of satellite inversion algorithms Common (static) ocean color inverse models are based on regression, or sometimes neural nets

•

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Simple case: G = a(φ)(440), S =Rrs(λ) Reality is generally more complicated: G = {phytoplankton, dissolved organics, suspended particles, etc} are all independent

Given a dataset of {G, S}, we can model the transfer function between S and G

S

S

f (·)

^ f -1 (·)

^ G

…

• •

G

…

Forward Model links ocean biogeochemistry and observed reflectance spectra

…



^ G

Other possibility (dynamic) is to use optimization in a spectral-matching framework

•

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Given S, optimize G to minimize error mse(S  Sˆ ), Sˆ  f (G) Ocean Color Inversion by Particle Swarm Optimization

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Spectral Matching Approach 



Goal of inversion is to retrieve a(φ)(440), a(cdm)(440), and bb(p)(555) from measured  a (440)  spectral reflectance    ( )  A simple forward model is created linking rˆrs ( )  F ( ),   a( cdm) (440) these three parameters to spectral reflectance  bb ( p ) (555)    [e.g., Sathyendranath et al. 1989]

 bb ( )   bb ( )    g 2   rrs ( )  g1   bb ( )  a( )   bb ( )  a( ) 

2

bbw(λ) [m-1] aw(λ) [m-1]

a( )  a w ( )  a (440)aˆ  ( )  a cdm (440)aˆ cdm ( ) bb ( )  bb w ( )  bb p (555)bˆb p ( )







1.2

a( ) ( )  a0 ( )  a1 ( ) ln a( ) (440)  a( ) (440)   

a(φ)(λ) [m-1]

1 0.8

-1

Normalized a [m ]

 555  a(cd m) ( )  a(cd m) (440 bˆb ()p )exp ( ) Scd m(  440) Y

0.6

High [chl a]

0.4 0.2

  r (440)   555  Low [chl a]  bˆb ( p ) ( )   Y  2.21  1.2 exp   0.9 rs rrs (555)         rrs (440)   Color Inversion by Particle Swarm Optimization  2.22004 1  1.2 exp   0.9 Ocean 21Y June rrs (555)    Y

0

-0.2 400

450

500 550 600 Wavelength [nm]

650

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Spectral Matching Approach (2) 

Forward model parameters (a(φ)(440), a(cdm)(440), and bb(p)(555)) are optimized to minimize error function between forward modeled reflectance and measured reflectance  1 n 2 f ( )  k 1 rrs (k )  rˆrs (k ) n

  

Parameters vary over several orders of magnitude Very nonlinear, problems with local minima Traditional search techniques rely on characteristics of search space, such as gradient

• • •

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Can lead to non-globally optimum solutions – get “stuck” Stochastic techniques such as genetic algorithms (GA) have been shown to do better in such problems Define a priori sub-ranges of parameters (i.e. low or high bb(p)(555), low or high a(φ)(440), etc.)

GA have performed well on this problem [Zhan et al. 2003]

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GA are slow – 400 x 400 pixel satellite image needs 160,000 optimizations PSO is fast! Ocean Color Inversion by Particle Swarm Optimization

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Overview       

Motivations for Ocean Color Inversion Ocean Color 101 Ocean Color Forward and Inverse Models Spectral Matching Approach Particle Swarm Optimization PSO-Based Inversion Results Conclusions

21 June 2004

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Particle Swarm Optimization 

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Particle Swarm Optimization (PSO) offers an alternative to GA Based on a population of potential solutions [Kennedy and Eberhart 1995]

•

• • 

Inspired by flocking birds and swarming insects Each bird influenced by its own success as well as the success of the flock or swarm The agents “fly” around the space of possible solutions

Each particle (agent) in the swarm represents a candidate solution

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Particle Swarm Optimization (2) 

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Each agent is a vector in D-dimensional space Each agent’s (i-th agent) trajectory update is simple

• • •

Inertia Direction of personal best, xi,best Direction of swarm best, xG,best

 xi (t  1)

 xi (t )

 xi ,best (t )

 xi (t  1)

 xi (t )

 xG ,best (t )



xi (t  1)    xi (t  1)  xi (t )  xi (t  1)       xi (t  1)    xi (t )  1  xi ,best (t )  xi (t )   2  xG ,best (t )  xi (t )



Φ are random components of update, as well as weighting factors

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Particle Swarm Optimization (3) 

Algorithm is simple

1.

Generate initial population of agents (candidate solutions) Evaluate each agent with objective function (such as MSE between measured and modeled spectra) If any particles have located new individual best solutions replace their previous xi,best, and keep track of the swarm global best xG,best Determine trajectories and new positions based on update rule If termination criteria (error goal or max iterations) is not met then go to 2 Optimum solution found is xG,best

2.

3.

4. 5.

6.

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PSO-Based Inversion Experiment 

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PSO Inversion is tested on a simulated dataset (n = 270) and compared against GA approach of Zhan et al. [2003] on the simulated dataset Simulated dataset is based on complex forward model

•

Model parameters are varied across wide range of values corresponding to realistic oceanic and coastal waters

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Dataset is hyperspectral (λ = 400–700 nm, 5 nm resolution)

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Swarm of 200 particles, 100 iterations, global topology

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More particles with global version of algorithm displayed good performance and speed characteristics

c1 = c2 = 2.05, with constriction coefficient

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PSO-Based Inversion Results

RMSE = 0.053 MADERR = 0.040 r2 = 0.91

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RMSE = 0.069 MADERR = 0.048 r2 = 0.83

Ocean Color Inversion by Particle Swarm Optimization

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PSO-Based Inversion Results (2)

RMSE = 0.162 MADERR = 0.093 r2 = 0.95

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RMSE = 0.409 MADERR = 0.247 r2 = 0.95

Ocean Color Inversion by Particle Swarm Optimization

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PSO-Based Inversion Results (3)

RMSE = 0.006 MADERR = 0.004 r2 = 0.99

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Ocean Color Inversion by Particle Swarm Optimization

RMSE = 0.016 MADERR = 0.010 r2 = 0.98

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Overview       

Motivations for Ocean Color Inversion Ocean Color 101 Ocean Color Forward and Inverse Models Spectral Matching Approach Particle Swarm Optimization PSO-Based Inversion Results Conclusions

21 June 2004

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Overview       

Motivations for Ocean Color Inversion Ocean Color 101 Ocean Color Forward and Inverse Models Spectral Matching Approach Particle Swarm Optimization PSO-Based Inversion Results Conclusions

21 June 2004

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Conclusions 

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PSO is a very simple and fast optimization algorithm

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Easy implementation (dedicated hardware – DSP?) Few user parameters Good global convergence

More agents helps to converge to global optima? Computational efficiency of more agents vs. neighborhood approaches Comparison on this dataset against GA approach

• •

PSO offers objectively “better” retrievals Order of magnitude faster (~300 seconds vs. ~10 seconds per retrieval)

Future work

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More complicated forward reflectance model Substantial speed increase is necessary for imagery (O(100) pixels/sec) Tests on in situ and satellite data Better comparison between various methods, such as GA, matrix inversion, NN, empirical, traditional optimization

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Questions?

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Activities sponsored by the NASA Earth Science Enterprise and the Maine Space Grant Consortium

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PSO Inversion Results 0

0

10

10

-1

-1

10

GA estimated

PSO estimated

10

-2

10

-3

10

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R2 0.849 RMSE 0.283 MADERR 0.184

-4

R2 0.559 RMSE 0.548 MADERR 0.351

-4

10 -3 10

-2

10

10

-1

10 -3 10

0

10

-2

10

a(440)

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-1

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a(440)

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PSO Inversion Results (2) 1

1

10

10

0

0

10

-1

GA estimated

PSO estimated

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10

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R2 0.869 RMSE 0.358 MADERR 0.151

-3

10

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10 -3 10

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-2

-1

10 acdm(440) + anap(440)

10

0

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R2 0.828 RMSE 0.598 MADERR 0.361

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10

-4

1

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10 -3 10

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-1

10 acdm(440) + anap(440)

Ocean Color Inversion by Particle Swarm Optimization

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1

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PSO Inversion Results (3) 0

0

10

10

-1

-1

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GA estimated

PSO estimated

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-2

10

-3

10

-3

10

R2 0.990 RMSE 0.077 MADERR 0.040

-4

10 -4 10

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-2

10

R2 0.864 RMSE 0.342 MADERR 0.210

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10

-3

-2

10 bbp(555)

-1

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0

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10 -4 10

10

-3

-2

10 bbp(555)

Ocean Color Inversion by Particle Swarm Optimization

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10

0

10

25

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