ISOEN 2011|Jin Huang|CSE@TAMU Overview Introduction What is active - - PowerPoint PPT Presentation

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ISOEN 2011|Jin Huang|CSE@TAMU Overview Introduction What is active - - PowerPoint PPT Presentation

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ISOEN 2011|Jin Huang|CSE@TAMU Overview Introduction What is active sensing? Infrared Fabry Perot interferometry Methods Non negative least squares Multi modal search Wavelength selection Results

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ISOEN 2011|Jin Huang|CSE@TAMU

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ICASSP 2013 | lab | CSE@TAMU 2

Overview

  • Introduction

– What is active sensing? – Infrared Fabry‐Perot interferometry

  • Methods

– Non‐negative least squares – Multi‐modal search – Wavelength selection

  • Results

– Chemical dataset – System behavior – Comparison with passive sensing

  • Discussion
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  • Perception is an active process

– “We not only see but we look, we not only touch we feel” ‐J.J. Gibson

  • Active sensor vs. active sensing

– Active sensor: a device that transmits energy in order to make measurements

  • E.g., radar, sonar

– Active sensing: a control strategy that dynamically adapts the sensor’s configuration as it interacts with the environments

  • E.g., changing camera viewpoints

What is active sensing?

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What is active sensing?

  • Analogy

– Guessing games

  • 20 questions, Pictionary, Battleship, Yes and no, Hangman

Question Answer Is your character real? Yes Isyour character male? Yes Is he alive? Yes Is he an actor? No Is he linked with sports? No Is he a musician? Yes Is he more than 50 years old? Yes Does he play the guitar? Yes Is he American? Yes Does he wear headgear? Yes Does he have messy hair? Yes Is it Bob Dylan? Yes

Vague Specific

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What is active sensing?

  • Analogy

– Guessing games

  • 20 questions, Pictionary, Battleship, Yes and no, Hangman

– Two seemingly conflicting problems at the same time

  • Find the right answer
  • Ask the right questions

– Advantage

  • Incorporate decision early in the signal processing pipeline
  • Reduce sensing costs ($, energy, time, computing power)
  • Lower sensor requirements
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Chemical Identity Concentration Sensor Reference Single Unknown Fixed MOX Gosangi et al. 2010 IEEE Sensors J Single Unknown Unknown (continuous) FPI Huang et al. 2012 IEEE Sensors J Mixture Known Unknown (discrete) MOX Gosangi et al. 2013 S&A B: Chemical Mixture Unknown Unknown (continuous) FPI Huang et al. 2013 ICASSP

Prior work

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ICASSP 2013 | lab | CSE@TAMU 12

Infrared absorption spectroscopy

IR source

  • log
  • IR spectrometer
  • Gas cell
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IR source Gas cell FPI d

  • Fabry‐Perot interferometer

, … ,

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  • Properties

– Absorption spectrum is linear (Beer’s law)

  • ⋮
  • ⋮
  • Concentration of each

chemical

  • +

Absorption spectrum

  • f the mixture
  • IR absorption

Absorption spectrum of each chemical

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ICASSP 2013 | lab | CSE@TAMU 22

  • ( )

( 1) ( 1)

Traditional mixture analysis

  • Problem definition

– Estimate , given (all wavelengths)

  • …

…

Wavelengths Chemicals

. . : 0

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  • Problem definition

– Estimate , but measuring one wavelength at a time

  • ( )

( 1) ( 1)

Active mixture analysis

  • …

…

Wavelengths Chemicals

. . : 0

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  • Problem definition

– Select the best wavelengths in to solve

  • ( )

( 1) ( 1)

Active mixture analysis

  • …

…

Wavelengths Chemicals

. . : 0

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  • …

…

  • Interpretation

– Each wavelength equals one element in

  • ( )

( 1) ( 1)

Active mixture analysis

Wavelengths Chemicals

. . : 0

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  • Interpretation

– Which allows us to use an additional row in

  • ( )

( 1) ( 1)

Active mixture analysis

…

…

Wavelengths Chemicals

. . : 0

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  • …

…

  • Interpretation

– Each new wavelength adds a new row in

  • ( )

( 1)

Active mixture analysis

( 1) Wavelengths Chemicals

. . : 0

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  • Issue

– The underlying linear system may be under‐determined

  • (2 )

( 1)

Active mixture analysis

(2 1)

  • …

…

Wavelengths Chemicals

. . : 0

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ICASSP 2013 | lab | CSE@TAMU 29

  • …

…

  • Solution

– Assume that is sparse

  • (2 )

( 1)

Active mixture analysis

(2 1)

  • Wavelengths

Chemicals

. . : 0

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ICASSP 2013 | lab | CSE@TAMU 30

  • …

…

  • Subset selection

– Select 1‐2 elements in

  • (2 )

( 1)

Active mixture analysis

(2 1) Wavelengths Chemicals

. . : 0

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ICASSP 2013 | lab | CSE@TAMU 31

  • …

…

  • Interpretation

– One element in implies one column in

  • (2 )

( 1)

Active mixture analysis

(2 1) Wavelengths Chemicals

. . : 0

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ICASSP 2013 | lab | CSE@TAMU 33

  • …

…

  • The selection is not unique

– A combinatorial problem ⇒ search

  • Active mixture analysis

. . : 0

Chemicals ( 1)

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Unimodal candidate selection

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Multimodal candidate selection

  • Iterative deepening

memory‐bounded heuristic search Iterative deepening memory‐bounded heuristic search

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Wavelength selection

Sensor Feature Selection Select Maximum variance Solutions:

  • ,

, … MM‐NNLS solver Unknown spectra b

  • Projection
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Case study

  • Dataset

– 100 chemicals from NIST WebBook (randomly chosen) – Wavelength range: 3 11.5 – Downsampled to 660 spectral lines – Added 2% Gaussian noise

  • Setup

– 3 chemicals mixture (sparsity 3%) – Search space 100 10 – We consider up to 10 alternate paths

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  • Step 1

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=1 Ground truth Measurement Projection Selected feature 10 20 30 40 50 60 70 80 90 100 l2 error Candidate error ranking

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  • Step 2

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=2 Ground truth Measurement Projection Selected feature 200 400 600 800 1000 1200 1400 1600 1800 l2 error Candidate error ranking

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  • Step 3

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=3 Ground truth Measurement Projection Selected feature 500 1000 1500 2000 2500 3000 3500 4000 l2 error Candidate error ranking

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  • Step 4

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=4 Ground truth Measurement Projection Selected feature 500 1000 1500 2000 2500 3000 3500 4000 l2 error Candidate error ranking

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  • Step 5

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=5 Ground truth Measurement Projection Selected feature 1000 2000 3000 4000 5000 6000 l2 error Candidate error ranking

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  • Step 6

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=6 Ground truth Measurement Projection Selected feature 1000 2000 3000 4000 5000 6000 7000 800 l2 error Candidate error ranking

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  • Step 7

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=7 Ground truth Measurement Projection Selected feature 1000 2000 3000 4000 5000 6000 l2 error Candidate error ranking

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  • Step 8

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=8 Ground truth Measurement Projection Selected feature 1000 2000 3000 4000 5000 6000 7000 l2 error Candidate error ranking

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  • Step 9

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=9 Ground truth Measurement Projection Selected feature 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 l2 error Candidate error ranking

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  • Step 10

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=10 Ground truth Measurement Projection Selected feature 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 l2 error Candidate error ranking

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  • Step 11

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=11 Ground truth Measurement Projection Selected feature 1000 2000 3000 4000 5000 6000 7000 8000 l2 error Candidate error ranking

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  • Step 12

3 4 5 6 7 8 9 10 11 2 4 6 x 10

  • 3

Wavelength (m) Absorption t=12 Ground truth Measurement Projection Selected feature 1000 2000 3000 4000 5000 6000 7000 8000 l2 error Candidate error ranking

Converged Converged

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Overall performance

  • Baseline: passive sensing

– Sequential forward feature selection – Trained to distinguish all 100 chemicals – Generates a fixed sequence of wavelengths

  • Experimental protocol

– Randomly pick chemicals and assign random concentrations

  • Concentration has to be significant (larger than 10%)

– Mixtures have from 1 up to 10 chemical components – Stopping criteria: same error threshold for both methods

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  • Number of measurements needed

– Fewer measurements means cost savings – For each # components we ran 100 examples

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  • Stability of the solution

– Measured with the condition number of ′

  • A measure of correlation among wavenumbers

– Higher condition # ⇒ higher correlation ⇒ less stability

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Discussion and future work

  • Discussion

– Multimodal search provides alternative candidates, which help tackle ill‐posed problems – Only a small fraction of candidate solutions are needed to reveal the uncertainty (by virtue of the back‐projection)

  • Future work

– Experimental validation on real FPI sensor – Improvements to the algorithm

  • Encouraging diversity to the candidate pool
  • Over‐fitting criteria for trace analysis
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Thank you Questions?