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This document and the information contained herein is the property of Saab AB and must not be used, disclosed or altered without Saab AB prior written consent. Enhancing Sonar resolution through smart signal processing UDT 2019 Sthlm A.

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

This document and the information contained herein is the property of Saab AB and must not be used, disclosed or altered without Saab AB prior written consent.

Enhancing Sonar resolution through smart signal processing

  • A. Gällström. L. Fuchs, C. Larsson

UDT 2019 Sthlm

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Outline

  • Compressive Sensing
  • The Inverse Problem
  • 𝑚1-norm
  • Propagators
  • Model
  • Examples
  • High Resolution from 1 ping measurement
  • Scatterer point representation
  • Multiple pings
  • Summary

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

  • H. Nyquist (1889-1976) and C. Shannon(1916-2001)

Nyquist-Shannon Sampling Theorem ”If a function contains no frequencies higher than B Hertz, it is completely determined by giving its ordinates to a series of points spaced 1/(2B) seconds apart.” (Wikipedia)

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Data compression

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  • Example: JPEG compression from 487 to 71 kB (16%)
  • Typical compression rate with a factor of 10
  • To much data is collected
  • Idea: Reduce data collection and compensate with signal processing
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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Compressive Sensing

  • Developments of theory for Compressive Sensing (CS)
  • Faster algorithms
  • Faster computers (flops/cpu)
  • Enabling practical use of Compressive Sensing (CS)
  • Pioneered by: Emmanuel Candés, David Donoho, Justin

Romberg and Terence Tao (2004)

  • CS means that less data is collected which is compensated by

using postprocessing

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Compressive sensing – early application MRI

  • Magnetic resonance imaging

(MRI)

  • Picture a shows an MRI-

image using complete data set and conventional data processing

  • Picture d shows an image

using 20% of data set (from a) and CS

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  • M. Lustig, D. Donoho, and J. M. Pauly. "Sparse MRI: The application of

compressed sensing for rapid MR imaging.“ Magnetic resonance in medicine 58, no. 6 (2007): 1182-1195.

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Inverse problems

  • Linear set of equations:

𝐵𝑦 = 𝑧 ൞ 𝑦 ∈ ℂ𝑂 𝐵 ∈ ℂ𝑛×𝑂 𝑧 ∈ ℂ𝑛

  • y is an observation/measurement, and we are trying to find x

(parameter)

  • Normally this set of equations are undetermined (m<<N) =>infinitely

many solutions (provided that there exists at least one)

  • Sonar: The reflected signal is used to determine position, speed,

target class…, i.e. parameters.

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Inverse problems

  • Underdetermined linear set of equations:

𝐵𝑦 = 𝑧

  • Possible to reconstruct signals under assumption of sparsity!

(A vector/matrix is sparse if most of its components are zero)

  • Efficient algorithms exists, in this work:

Quadratically constrained l1-minimization problem: min 𝑦 1 𝑡𝑣𝑐𝑘. 𝑢𝑝 𝐵𝑦 − 𝑧 2 ≤ 𝜏 𝜏 related to SNR (other variants exist: LASSO, Dantzig selector, …)

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

𝑚0-, 𝑚1- and 𝑚2-norms

  • Norm: total size or length
  • 𝑚2: ”straight-line” – Euclidian distance 𝑦 2 =

σ𝑗 𝑦𝑗

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  • 𝑚0 : Sparsity –

𝑦 |1 = #(𝑗|𝑦𝑗 ≠ 0) (total number of non-zero elements in a vector. Useful for finding the sparsest solution. However: minimization is regarded as NP-hard.

  • 𝑚1: 𝑦 1 = σ𝑗 𝑦𝑗
  • 𝑚1relaxed 𝑚0:used in Compressive sensing. Not as smooth as 𝑚2,

but this problem is better and more unique than the 𝑚2-

  • ptimization.

The optimization road is convex optimization.

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Compressive sensing

  • Sonar
  • Point scatter model
  • Back-propagator
  • Forward-propagator

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Model (Point scatterer)

  • Isotropic, frequency independent point scatterer as model.
  • 𝐵𝑦 = 𝑧
  • A: signal generator (from point scatterer to element signals)

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Back-propagator

  • Classical Delay-And-Sum:

ො 𝛿 𝑠 = 1 𝑂 ෍

𝑜=1 𝑂

𝐵𝑜𝑡𝑜 𝑢𝑜 𝑠

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Forward-propagator

Signal observed at time 𝑢 and position 𝑠 emitted from a point scatterer at 𝑠′: 𝑡 𝑢, 𝑠 = 𝐵 𝑢 − 𝑠 − 𝑠′ 𝑑 𝑠 − 𝑠′ 2 𝑓

𝑗𝜕𝑢 𝑢− 𝑠−𝑠′ 𝑑

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Outline

  • Synthetic Aperture Sonar
  • Compressive Sensing
  • Examples
  • High Resolution from 1 ping measurments
  • Robustness
  • Modell from different pings
  • Autofocus – position based
  • Autofocus – phase based
  • Summary

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Measurement setup

  • Sapphires
  • SAS resolution <4x4 cm
  • Fresh water lake: Vättern

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Normal resolution from 1 ping measurement

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Normal Resolution from 1 ping measurment

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min 𝑦 1 𝑡𝑣𝑐𝑘. 𝑢𝑝 𝐵𝑦 − 𝑧 2 ≤ 𝜏 Visualize with longer array

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Enhanced resolution

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min 𝑦 1 𝑡𝑣𝑐𝑘. 𝑢𝑝 𝐵𝑦 − 𝑧 2 ≤ 𝜏 𝑡𝑏𝑛𝑓 𝑠𝑓𝑡𝑝𝑚𝑣𝑢𝑗𝑝𝑜

Same data used for both this images

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Enhanced resolution

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min 𝑦 1 𝑡𝑣𝑐𝑘. 𝑢𝑝 𝐵𝑦 − 𝑧 2 ≤ 𝜏 𝑠𝑓𝑡: 𝑦2

Same data used for both this images

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Enhanced resolution

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min 𝑦 1 𝑡𝑣𝑐𝑘. 𝑢𝑝 𝐵𝑦 − 𝑧 2 ≤ 𝜏 𝑠𝑓𝑡: 𝑦4

Same data used for both this images

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Enhanced resolution

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min 𝑦 1 𝑡𝑣𝑐𝑘. 𝑢𝑝 𝐵𝑦 − 𝑧 2 ≤ 𝜏 𝑠𝑓𝑡: 𝑦8

Same data used for both this images

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Enhanced resolution

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min 𝑦 1 𝑡𝑣𝑐𝑘. 𝑢𝑝 𝐵𝑦 − 𝑧 2 ≤ 𝜏 𝑠𝑓𝑡: 𝑦16

Same data used for both this images

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Modell

  • Visualization of point scatterers based on one

ping

  • Sparsivity: ~10%

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

SAS

1 ping

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

SAS

2 pings

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

SAS

3 pings

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

SAS

~30 pings

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Several pings

Three pings used, with no overlap (and no autofocus), coherently added

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Several pings

Three pings used, with no overlap (and no autofocus), incoherently added

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Several pings

Three pings used, with no overlap (and no autofocus), processed using CS and incoherently added

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

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CS and incoherently added Incoherently added Coherently added

Same data from 3 non-overlapping pings without autofocus

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Summary

  • Compressive sensing utilizing the sparsity in sonar data is an

interesting and promising tool

  • Examples:
  • Enhancing resolution in one-ping images
  • Combining multiple pings

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COMPANY RESTRICTED | NOT EXPORT CONTROLLED | NOT CLASSIFIED Andreas Gällström | Document Identification | Issue 1

Thank you