Neural parametric steered mixture of experts for inverse problems

Image denoising constitutes a fundamental inverse problem in computational imaging, serving as a critical preprocessing step across medical imaging, computer vision, and scientific visualization. Traditional variational approaches including Total Variation (TV) regularization, Non-Local Means (NLM), and the Block-matching and 3D filtering (BM3D) algorithm have demonstrated efficacy over three decades, yet struggle with the preservation-restoration trade-off inherent to diagnostic feature extraction. This challenge intensifies in medical imaging due to complex anatomical morphologies and heteroscedastic noise characteristics across modalities, where speckle phenomena and signal-dependent degradations violate Gaussian assumptions; reconstruction fidelity is therefore a relevant consideration for downstream image interpretation. The established Steered Mixture of Experts (SMoE) framework exhibits proven performance in compression and edge-preserving applications through adaptive kernel selection, yet encounters fundamental limitations when confronting heavy-tailed noise distributions characteristic of medical imaging modalities. These constraints manifest across diverse acquisition techniques including Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Electron Microscopy (EM), and Optical Coherence Tomography (OCT), where modality-specific noise processes fundamentally disrupt statistical assumptions underlying traditional Gaussian kernel formulations. Furthermore, conventional iterative optimization schemes impose computational burdens incompatible with real-time clinical workflows. This research introduces a Neural Steered Mixture of Experts (N-SMoE) architecture that reconceptualizes inverse problem solving through deep learning integration for medical imaging applications. Our methodology transcends traditional Gaussian kernel limitations by implementing heterogeneous mixture models that naturally accommodate heavy-tailed and impulsive noise characteristics inherent to clinical data across multiple modalities. This theoretical advancement addresses critical limitations where conventional distributional assumptions prove inadequate for capturing complex degradation patterns observed in medical imaging scenarios. The methodological innovation centers on sophisticated Multi-Model Inference (MMI) that synthesizes information from multiple SMoE models operating across local and global block neighborhoods through learned feature representations. This fusion strategy leverages successful block-matching paradigms while extending capabilities through neural network architectures. Rather than relying on computationally intensive iterative schemes, our framework employs ultra-fast autoencoder-based parameter estimation that satisfies stringent timing requirements of clinical environments without compromising reconstruction quality. The N-SMoE architecture incorporates sophisticated encoder networks featuring Multilayer Laplacian Resizers (MLR), residual blocks for hierarchical feature learning, attention mechanisms for adaptive feature weighting, and Multi-Head Self-Attention (MHSA) pooling for global context aggregation. Training utilizes a comprehensive Stochastic Degradation Model (SDM) that simulates diverse data distributions and noise characteristics across medical imaging modalities. Critically, Generative Adversarial Network (GAN)-based adversarial training enhances perceptual quality through feature-level optimization, enabling the network to learn robust representations that generalize across different imaging conditions and pathological variations. Experimental validation demonstrates substantial performance improvements across multiple medical imaging modalities. Comprehensive evaluation on datasets spanning CT, MRI, EM, and OCT reveals that N-SMoE variants consistently achieve superior performance rankings. The proposed Block-Matching Steered Mixture of Experts (BM-SMoE) methodology achieves notable reconstruction gains, with improvements of 1.93 dB in Peak Signal-to-Noise Ratio (PSNR) and 0.09 in Structural Similarity Index Measure (SSIM) compared to the established BM3D algorithm. These quantitative improvements translate into improved fidelity of anatomical structures relevant to subsequent image-based analysis; the present evaluation is restricted to image-quality metrics and does not include clinician reader studies or task-based diagnostic-accuracy assessment. The edge-aware gating networks developed within this framework represent significant advancement in preserving anatomical boundaries while maintaining smooth tissue transitions through learned spatial priors. Unlike conventional approaches that treat edge preservation and noise reduction as competing objectives, our method achieves simultaneous optimization through carefully designed neural architectures operating with minimal computational overhead. This capability proves particularly valuable across medical imaging modalities, where preservation of fine structural details differentiates accurate diagnosis from missed pathology. Beyond traditional denoising applications, the research extends to Single Image Super-Resolution (SISR) tasks critical in modern medical imaging workflows. The framework demonstrates remarkable adaptability by enhancing spatial resolution without requiring retraining for different magnification factors through learned upsampling operators. Adjustable sharpness control mechanisms expose a user-tunable trade-off between smoothing and edge retention at inference time. In conclusion, this dissertation contributes an N-SMoE framework that addresses statistical-modelling and computational limitations of prior SMoE variants for medical image restoration across multiple modalities. The reported reconstruction-fidelity improvements across CT, MRI, EM, and OCT are evaluated on synthetic-degradation benchmarks and public datasets; claims regarding clinical utility, diagnostic accuracy, or patient outcomes would require independent external validation and task-based or reader-based assessment, which are outside the scope of the present work.