Yusuf Talha Basak, Mehmet Ozan Unal, Metin Ertas et al.
Although Total Variation (TV) performs well in noise reduction and edge preservation on images, its dependence on the lambda parameter limits its efficiency and makes it difficult to use effectively. In this study, we present a Learnable Total Variation (LTV) framework that couples an unrolled TV solver with a data-driven Lambda Mapping Network (LambdaNet) predicting a per-pixel regularization map. The pipeline is trained end-to-end so that reconstruction and regularization are optimized jointly, yielding spatially adaptive smoothing: strong in homogeneous regions, relaxed near anatomical boundaries. Experiments on the DeepLesion dataset, using a realistic noise model adapted from the LoDoPaB-CT methodology, show consistent gains over classical TV and FBP+U-Net: +2.9 dB PSNR and +6% SSIM on average. LTV provides an interpretable alternative to black-box CNNs and a basis for 3D and data-consistency-driven reconstruction.