Learnable Total Variation with Lambda Mapping for Low-Dose CT Denoising

While Total Variation (TV) excels in noise reduction and edge preservation, its reliance on a scalar regularization parameter limits adaptivity. In this study, we present a Learnable Total Variation (LTV) framework coupling an unrolled TV solver with a LambdaNet that predicts a per-pixel regularization map. The proposed framework is trained end-to-end to optimize reconstruction and regularization jointly, yielding spatially adaptive smoothing. Experiments on the DeepLesion dataset, using realistic LoDoPaB-CT simulation, show consistent gains over classical TV and FBP+U-Net, achieving up to$\mathbf{+ 3. 7} \mathbf{~ d B}$PSNR and$\mathbf{8 \%}$relative SSIM improvement. LTV provides an interpretable alternative to black-box CNNs for low-dose CT denoising.