Self-Supervised Multibeam Sonar Restoration via Coherent Forward Modeling
Multibeam imaging sonar is widely used for underwater perception, but its intensity images are degraded by coupled coherent speckle and system-induced blur, and clean reflectivity ground truth is almost never available. This paper derives the conditional-mean forward operator $A x = x * |h|^2$ from a stochastic coherent image-formation model and uses it to train a self-supervised reconstruction network from registered multi-frame observations. By projecting one frame's latent reconstruction through $A$ and matching it to a second registered frame, then regularizing with an adapted robust equivariant imaging loss, the framework targets joint despeckling and deblurring without any clean targets. The work matters because it replaces ad hoc intensity-domain speckle models with a physics-consistent inverse problem for real sonar platforms.
The paper offers a principled physics-based route to sonar restoration. The derivation of the conditional-mean forward model and the paired forward prediction error (PFPE) metric are strong conceptual contributions, and the ablation honestly shows that the physics-consistency loss alone collapses without REI regularization: 'a physics-consistency-only ($\mathcal{L}_{\mathrm{PC}}$-only) variant improves PFPE but yields nearly zero ENL and extremely large $D_{\mathrm{EPI}}$' (Section IV-D). However, the framework leans on an idealized conditional-mean assumption for paired frames and an exactly known, locally shift-invariant PSF, neither of which is rigorously validated on real data. Moreover, deblurring is only assessed indirectly through measurement-domain consistency and edge proxies, leaving open whether the network truly recovers sharper latent reflectivity.
The derivation from the coherent observation model $y = |(\sqrt{x} \cdot g) * h|^2$ to the conditional mean $\mu(x) = x * |h|^2$ is analytically clean and correctly identifies that speckle correlation and blur are jointly induced by the coherent PSF (Section II, Eq. 14-15). The PFPE metric is a well-reasoned, ground-truth-free evaluation proxy that tests forward-prediction consistency under a held-out paired observation (Section IV-A, Eq. 28-29). At inference, the method is compact and fast: it uses the same lightweight U-Net backbone as PI-SSD and runs in 0.043 s per 512x512 image, which exceeds the acquisition frame rates of both tested datasets (Section IV-F, Table II).
The self-supervised loss relies on the assumption $\mathbb{E}[y_2 \mid x, y_1] \approx \mathbb{E}[y_2 \mid x] = \mu(x)$ (Section III-C, Eq. 7), yet the supplementary correlation analysis shows that at frame gap 1 on the Boat dataset only 56.59% of homogeneous ROIs achieve $r < 0.5$, meaning a large fraction of training pairs retains substantial speckle correlation that breaks the required conditional independence (Supplementary Table III). The PSF is assumed exactly known and locally shift-invariant—'$h:=h(t,\vartheta)=R(t)B(\vartheta)$' with a 'local shift-invariant approximation of $h$ evaluated around the central beam direction' (Section II)—but the conclusion admits 'forward-model mismatch' is a remaining limitation with no sensitivity analysis provided. Furthermore, the deblurring claim is evaluated only indirectly: 'deblurring is evaluated indirectly through consistency with the sonar forward model and preservation of visible structures' (Section IV-A); no metric directly quantifies removal of the PSF blur from latent reflectivity, and edge preservation relative to the already-blurred observed image is a weak proxy for true sharpness recovery.
Evidence from two real datasets suggests the proposed method improves paired forward prediction over baselines, with aggregate PFPE improvement 14.10% on Boat versus 13.39% for the next best B2UB (Table I). The authors are commendably careful to note that 'PFPE is interpreted under a common latent-reflectivity hypothesis rather than as a full-reference quality metric' (Section IV-A). This caution is warranted: SS-BSN and LG-BPN achieve higher ENL but much larger $D_{\mathrm{EPI}}$, indicating oversmoothing rather than accurate reflectivity recovery. The comparison would be more convincing if supplemented by controlled simulations with known reflectivity to confirm that better PFPE maps to genuine deblurring, because the current evaluation cannot disentangle speckle suppression from blur removal.
The authors report the network architecture (U-Net via deepinv), optimizer settings (Adam, learning rate $1\times10^{-4}$, weight decay $5\times10^{-7}$), PSF generation parameters, and pairing thresholds (Section IV-C). However, neither the raw sonar datasets nor the training code is released. The PSF is synthesized from nominal sensor geometry, but real multibeam PSFs vary with environment and calibration. Hyperparameters such as the REI weight '$\alpha=0.03$ for Boat and $\alpha=0.05$ for Underwater Structure, based on validation performance' are dataset-specific and selected without ground truth, making the selection criterion hard to replicate. Independent reproduction is blocked by unavailable data, unshared code, and the lack of any sensitivity analysis to PSF mismatch or registration error.
Multibeam imaging sonar produces intensity images degraded by coherent speckle and system-induced blur, while clean reflectivity targets are rarely available. Existing despeckling methods often rely on simplified intensity-domain noise models, synthetic clean targets, or blind-spot self-supervision, and typically do not jointly model deblurring and speckle suppression. We propose a physics-consistent self-supervised framework for joint despeckling and deblurring of multibeam imaging sonar. A stochastic coherent image-formation model yields a conditional-mean forward operator that relates latent scene reflectivity to expected intensity through the squared magnitude of the system point spread function. We then use registered multi-frame sonar sequences to train without clean ground truth images, showing that, under an idealized inter-frame conditional-mean condition, the expected paired loss equals the corresponding forward-prediction loss up to a network-independent constant. To stabilize the ill-conditioned inverse problem, we further adapt robust equivariant imaging using stochastic coherent simulation and introduce a paired forward prediction error metric for ground-truth-free evaluation. Experiments on two real multibeam sonar datasets demonstrate a favourable balance between forward-prediction agreement, homogeneous-region speckle suppression, and preservation of visible structural boundaries compared with representative baselines.
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