Implicit Neural Speckle Denoising

This letter introduces a physics-informed self-supervised framework for sonar image despeckling that reformulates despeckling as residual consistency in the homomorphic log domain. By constraining the log-ratio residual to obey multiplicative speckle statistics, the proposed method eliminates the need for clean supervision while preventing degenerate identity solutions. A variance-targeted statistical loss combined with edge-aware structural regularization and median-guided curriculum stabilization enables effective speckle suppression with preserved structural fidelity. This formulation along with a lightweight neural network achieves state-of-the-art performance across multiple real sonar datasets and demonstrates excellent cross-dataset robustness, while remaining suitable for real-time deployment.

Ultrasound B-mode imaging commonly suffers from speckle noise and artifacts, requiring a delicate balance between contrast, resolution, and preservation of anatomical structures. Although recently developed despeckling methods have achieved some progress, supervised learning approaches remain fundamentally limited by the ground truth paradox, which arises from the absence of noise-free, ground truth reference images in in vivo scenarios. Existing unsupervised diffusion-based methods typically enforce data consistency directly in the nonlinear log-compressed domain, which can disproportionately amplify background artifacts when mapped back to the envelope domain. To overcome these limitations, we propose an uncertainty-guided null-space diffusion (UGNS) framework, a novel label-free solution that enforces consistency correction on a stabilized positive-envelope proxy obtained via inverse log compression. The proposed UGNS introduces several technical novelties: (a) extraction of a structural prior in the stabilized envelope domain to produce a robust signal envelope that preserves anatomical structure, (b) development of an adaptive range-null reconstruction mechanism that uses an adaptive weight mask to preserve tissue regions via range-space projection, and (c) introduction of uncertainty-guided fusion in an adaptive way to mitigate sampling variability. Extensive and comparative experiments were conducted using the PICMUS benchmark and in vivo datasets. The results demonstrate that UGNS achieves competitive generalized contrast-to-noise ratio (gCNR) values across diverse datasets. In addition, it is successfully validated that UGNS effectively suppresses speckle noise while preserving fine spatial resolution. Code is available at https://github.com/yousirong/UGNS.git.

MG-SpaIR is a training-data-free framework for restoring a clean image from a single observation corrupted by a mixture of blur, downsampling, noise, and missing pixels. Building on implicit neural representations (INRs), we introduce a multi-grade coarse-to-fine residual hierarchy that progressively refines the reconstruction across resolution grades, improving representational fidelity and mitigating spectral limitations. To stabilize reconstruction optimization and suppress INR-induced artifacts, we further propose an explicit sparse proximal regularization (e.g., $\ell_0$-type) applied directly in the high-resolution image domain, which discourages spurious high-frequency patterns while preserving sharp structures. The resulting optimization is solved efficiently via a multi-grade proximal alternating scheme, and we establish convergence guarantees for the associated updates under standard regularity conditions. Experiments on mixed-degradation benchmarks demonstrate that MG-SpaIR consistently outperforms strong training-data-free baselines such as Deep Image Prior, providing a stable, interpretable, and data-efficient alternative to conventional learning-based restoration methods.