Parameter-Efficient CT Reconstruction via Deep Graph Laplacian Regularization

Computed tomography (CT) plays a crucial role in medical diagnosis, but minimizing radiation exposure while maintaining image quality remains a critical challenge. Low-dose CT (LDCT) protocols reduce radiation risks but inevitably suffer from severe noise and artifacts that compromise diagnostic accuracy. While existing deep learning methods have achieved promising results, there remains a continuous quest for generative paradigms that intrinsically capture global-to-local structural dependencies to better preserve fine anatomical details. To this end, we propose DeVAR, a novel generative framework that applies visual autoregressive modeling (VAR) to LDCT denoising for the first time. Conditioned on global context provided by LDCT prefix tokens, DeVAR progressively generates discrete token maps of the target normal-dose CT (NDCT) via next-scale prediction. Because quantization inherently discards high-frequency information, we introduce a residual refiner to capture subtle anatomical structures beyond the capacity of a discrete codebook. Finally, empowered by a dual-representation hybrid training strategy, our hybrid NDCT decoder seamlessly integrates continuous and discrete latents to reconstruct high-fidelity, detail-preserved images. Extensive experiments on two public datasets demonstrate that DeVAR consistently achieves superior qualitative and quantitative performance compared to state-of-the-art LDCT denoising methods.

Laplacian-regularized minimization is fundamental in signal processing and machine learning, but is limited by the dense and ill-conditioned nature of the graph Laplacian pseudoinverse. While the Laplacian itself is sparse, its pseudoinverse is dense and often ill-conditioned, rendering direct computation impractical at scale. Moreover, pseudoinverse learning is more challenging than Laplacian learning. To address this challenge, this paper considers the setting where the graph Laplacian is given and proposes a Difference-of-Convex Regularizer (DCR) graph learning framework that approximates the spectral action of the Laplacian pseudoinverse without direct inversion via regularized Maximum Likelihood Estimation (MLE). By reformulating Laplacian-Regularized Nonnegative Least Squares (LR-NNLS) through a dual representation, DCR decouples pseudoinverse learning from instance-specific inference and enables efficient primal solution reconstruction via a differentiable dual-guided learning scheme. We establish theoretical guarantees on stability and the existence of a unique fixed point for DCR algorithm. Numerical experiments demonstrate improved performance over convex solvers and graph filtering baselines and robust performance across diverse graph topologies.

While deep learning-based denoising has become widely adopted in low-dose CT, conventional models use generic architectures designed for natural images, failing to account for non-stationary and spatially correlated CT noise characteristics. To address this, we propose an Efficient Noise COntext-aware REpresentation (ENCORE) framework that explicitly leverages CT noise characteristics and anatomical features. First, we reformulate the noise synthesis procedure based on a realistic noise distribution beyond the conventional Gaussian approximation, establishing a rigorous foundation for training pair generation. Next, we extract local noise power and correlation contexts to guide the denoising process. To fully leverage the potential of noise context, we propose a FlyingConv module, which adaptively changes convolution weights for each local image region. Notably, our approach demonstrates substantial gains in both denoising quality and computational efficiency. Furthermore, manipulating the intensity of the noise context maps at inference time enables zero-shot conditional denoising, allowing for dynamic control over the output image texture. The entire pipeline is available at https://github.com/minwoo-yu/ENCORE.git