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Self-Supervised Deconvolution of In-Air Sonar Images Using Sensor Ego-Motion

Jan Steckel

arXiv:2610.09682v1eess.SP

TL;DR

Sparse-array in-air sonar images have sidelobes and angular resolution that degrades toward the field-of-view edges, while deconvolution depends on a difficult-to-calibrate imaging-chain PSF. The paper learns deconvolution and a physics-structured PSF from sonar data and robot odometry using acoustic-flow warping. In simulation, it achieves 5° to 6° resolution across the field of view and concentrates 64% of image energy around true echoes.

  • Problem

    DAS sonar images have high sidelobes and resolution that degrades toward the field-of-view edges, while deconvolution requires a complete PSF that is difficult to calibrate and is ambiguous with scene structure from a single image.

    Source: §I · p. 1

  • Method

    A network predicts reflectivity, which is warped using robot odometry and acoustic flow and rendered through a learned, physics-structured model of the imaging chain.

    Source: §I · p. 1, §II · p. 2

  • Results

    5° to 6° constant resolution over the full field of view, with 64% of image energy around true echoes against 59% for the best DMAS variant and 62% for CLEAN with the true PSF.

    Source: §V · p. 4

  • Takeaways & Limitations

    Because it requires no ground truth, the method can be trained directly on recordings of the real sensor.

    Source: §V · p. 4

Abstract

from arXiv · show

Broadband in-air sonar sensors with a sparse microphone array form images through delay-and-sum beamforming, which leaves high sidelobes and an angular resolution that degrades strongly towards the sides of the field of view. Deconvolving these images requires access to the point-spread function of the complete imaging chain, including the emitter spectrum and directivity and the array imperfections. In practice, these aspects are hard to calibrate for. In this letter, we propose a self-supervised method that learns a deconvolution network together with a physics-structured model of the point-spread function, requiring only the sonar data itself and the odometry of a moving robot on which the sensor is mounted. Using acoustic flow warping, the internal representation of the model is warped and subsequently rendered through the learned point-spread function. This is then compared to the measured images under a speckle likelihood in accordance with the statistical model of image formation. In simulation, the learned model recovers the unknown emitter directivity, and the deconvolved images reach a constant angular resolution of 5 to 6 degrees over the full field of view, against 12 to 30 degrees for delay-and-sum and 7 to 23 degrees for delay-multiply-and-sum with coherence factor. The method outperforms classical deconvolution with the nominal point-spread function, and even outperforms CLEAN with the true one.

I. INTRODUCTION

Sparse-array N-AIR sonar images have sidelobes and resolution that worsens toward the field-of-view edges, while deconvolution needs a complete imaging-chain PSF that is difficult to calibrate. The paper uses robot motion to learn deconvolution and a physics-structured PSF from sonar data and odometry, alongside a model of how reflectivity produces energyscapes.

I. INTRODUCTION

  • With 32 microphones, DAS images have high sidelobes and a main lobe that widens toward the field-of-view edges.Larger arrays add size, power, and price, while regular arrays work well only in narrowband formulations.Source: §I · p. 1
  • Deconvolution methods and neural networks need an accurate PSF or ground-truth source maps, but an active-sonar PSF also depends on emitter properties and microphone mismatch.From a single image, the PSF and scene are fundamentally ambiguous.Source: §I · p. 1
  • Robot motion supplies supervision because reflectors follow acoustic flow while sidelobes follow the reflector that generated them.The proposed network maps DAS energyscapes to sparse reflectivity, warps that representation using odometry, and renders it through a learned imaging-chain model.Source: §I · p. 1

II. IMAGING MODEL

  • The imaging model forms a PSF from simulated microphone signals beamformed at nominal positions, then predicts an energyscape from reflectivity while neglecting interference between reflectors in the same range cell.Its learnable parameters include microphone gains and positions, emitted spectrum, sensor directivity, emitter position, and air absorption; the gain a0 is fixed from the data because only its product with reflectivity enters the model.Source: §II · p. 2

III. SELF-SUPERVISED DECONVOLUTION

The method trains a network to predict reflectivity from an energyscape and uses subsequent measurements as a self-supervised signal. Acoustic-flow warping carries the prediction to later poses before rendering and comparison.

III. SELF-SUPERVISED DECONVOLUTION

  • The network maps an energyscape to a geometric reflectivity map, which is rendered through the forward model and compared with the measured energyscape.The reflectivity map is also warped to the poses of subsequent pulses and compared with their measured energyscapes.Source: §III · p. 2
  • Warping the internal reflectivity map to subsequent pulse poses provides the self-supervised learning signal for deconvolution.The passage identifies this step as essential to learning deconvolution without ground truth.Source: §III · p. 2
  • The method compares both the rendered prediction at the current pose and the warped prediction at later poses with measured energyscapes.Source: §III · p. 2

A. Acoustic-flow warp

Acoustic flow describes how a static reflector moves through the 2D image as the sensor platform moves. The method uses odometry and gyroscope measurements to warp its reflectivity map between pulses.

A. Acoustic-flow warp

  • For a forward-facing sensor, a static reflector moves through the 2D image according to acoustic flow determined by platform linear and angular velocity.Source: A. Acoustic-flow warp · p. 2
  • Wheel odometry and gyroscope measurements determine the motion between pulses, which is integrated as a rigid transformation for each step.Source: A. Acoustic-flow warp · p. 2
  • A fixed, physics-based warp moves each reflectivity-map cell with backward mapping and linear interpolation; a mask excludes cells entering the field of view.The forward model handles changes in PSF and spreading loss with position.Source: A. Acoustic-flow warp · p. 2

B. Loss terms

The loss combines reconstruction and motion-based prediction under a speckle model, with regularizers for concentrated reflectors and plausible sensor directivity. Prediction helps distinguish true reflectors from sidelobes because sidelobes follow the motion of the reflector that produced them.

B. Loss terms

  • The speckle likelihood models measured power around the incoherent mean; its heavy-tailed form behaves like squared log error for small deviations and absolute error for large ones.This limits the influence of unexplained power, such as sidelobes entering the field of view.Source: B. Loss terms · pp. 2–3
  • The prediction term resolves reconstruction ambiguity because a sidelobe mistaken for a reflector follows the wrong acoustic flow and predicts future energyscapes incorrectly.The reconstruction term alone can be satisfied by maps that explain sidelobes as reflectors.Source: B. Loss terms · p. 3
  • The sparsity penalty favors concentrated reflectors, while an L1 penalty performs equally well.The square-root penalty uses ϵ = 10^-4.Source: B. Loss terms · p. 3
  • Total-variation and squared-hinge sensor priors regularize transducer gain across neighboring directions and keep it below its on-axis value plus 3 dB.The total-variation penalty applies to gain in dB.Source: B. Loss terms · p. 3
  • The network jointly minimizes a weighted sum of reconstruction, prediction, sparsity, total-variation, and axis penalties over network weights and forward-model parameters.The supplied weights are λsp = 0.2, λtv = 0.01, and λax = 0.1.Source: B. Loss terms · p. 3

C. Network and output resolution

The network uses directional, range, and all-direction mixing branches to process compressed energyscapes. Its output is blurred with a fixed Gaussian kernel that sets a uniform output resolution.

C. Network and output resolution

  • Six blocks with 48 channels each combine dense mixing over all directions, order-3 Chebyshev graph convolution over neighboring directions,, and dilated convolution over range; the network takes compressed energyscape 10 log10(1+ P/N0) and range as inputs.Dense mixing uses a learned M × M matrix initialized as the identity.Source: C. Network and output resolution · p. 3
  • The clean reflectivity map is formed by blurring the nonnegative network output with a fixed Gaussian kernel H of 1.5° in azimuth and 0.7 range cells.The kernel is a design choice that sets uniform output resolution across the field of view.Source: C. Network and output resolution · p. 3

A. Simulation setup

The simulation evaluates a 32-microphone sonar and moving robot across rooms with realistic echoes, odometry noise, and unknown sensor mismatches. The authors compare the learned method with beamforming and iterative deconvolution baselines using echo localization and resolution metrics.

A. Simulation setup

  • The simulated eRTIS sensor uses 32 microphones and an emitter with a band-pass response peaking at 45 kHz and frequency-varying directivity.The true array deviates from nominal geometry and microphone gains, while the emitter axis is misaligned; these mismatches are unknown to the deconvolution model.Source: A. Simulation setup · pp. 3–4
  • The robot traverses 24 rooms—20 for training and 4 for validation—with 500 pulses each, 20–30 echoes per pulse, 10% odometry noise, and 0.15° gyroscope noise.Paths are smooth, with motion of 8 cm per pulse.Source: A. Simulation setup · p. 4
  • Training runs for 15,000 AdamW steps, and evaluation compares DMAS variants, DAMAS, Richardson-Lucy, and CLEAN using nominal or true PSFs.Metrics include image-energy concentration around the strongest true echoes, contrast, isolated-echo width, peak error, and detection rate.Source: A. Simulation setup · p. 4

B. The learned PSF

The learned PSF reproduces the main lobe, its widening toward the field edges, and the first sidelobes, while recovering the emitter-directivity sensitivity curve that the nominal model cannot know.

B. The learned PSF

  • The learned PSF matches the true PSF with 0.95 dB-correlation and 1.3 dB median error, and recovers the 8.2 dB sensitivity drop toward 85° within 0.5 dB.The nominal PSF matches the true shape about as well (0.95 correlation, 1.2 dB median error) but cannot know the sensitivity curve.Source: B. The learned PSF · p. 4

C. Image quality

The deconvolved output maintains 5°–6° resolution, while DMAS broadens from 7° to over 20° toward the field-of-view sides. It also concentrates more image energy around true echoes than the listed alternatives.

  • 64% of image energy is concentrated around true echoes, versus 59% for the best DMAS variant, 56% for nominal-PSF classical deconvolution, and 62% for CLEAN with the true PSF.Source: C. Image quality · p. 4
  • All methods detect at least 96% of isolated echoes, with median peak error at most 1°.Source: C. Image quality · p. 4
  • DMAS suppresses DAS sidelobes, but its main lobe widens from 7° to over 20° toward the sides, whereas the deconvolved output keeps 5° resolution.Source: C. Image quality · p. 4

D. Ablations

The conclusion reports constant 5°–6° resolution over the field of view and 64% image energy around true echoes in simulation. Ablations show the prediction term and heavy-tailed likelihood matter, while performance changes little with a rippled transmit spectrum.

D. Ablations

  • Without the prediction term, output stays at DAS level (Enear 0.33); fixing the forward model at nominal design gives 0.59, as does squared error, while exponential likelihood gives 0.51.The L1 penalty performs on par with the square root.Source: D. Ablations · p. 4
  • With transmit-spectrum ripples up to ±10 dB, scores are 0.64 when trained on those data and 0.63 for the smooth-spectrum-trained model.Source: D. Ablations · p. 4

V. CONCLUSION AND FUTURE WORK

  • 5°–6° resolution and 64% image energy around true echoes are achieved in simulation, versus 59% for the best DMAS variant and 62% for CLEAN with the true PSF.Source: §V · p. 4
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