用稀疏加平滑的图像块模型，提升图像重建精度。
Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction
- 将图像块稀疏表示与无约束平滑结合，优化可解释性。
- 在去噪、超分辨率和磁共振成像中均优于传统方法。
- 基于学习优化字典与正则参数，适合追求高可解释性的研究者。
我们针对成像中的反问题求解，将图像块的稀疏表示与无约束平滑相结合，实现重建过程的直观解释。通过构建双层优化框架，内层使用经典算法，外层利用监督学习优化字典和正则化参数，借助隐式微分与梯度优化完成训练。在去噪、超分辨率及压缩感知磁共振成像任务中评估该方法，对比经典模型与基于深度学习的方法，结果表明其始终优于前者，并在某些情况下超越后者。
原文摘要 · Abstract (English)
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate the optimization as a bilevel problem. The inner problem deploys classical algorithms while the outer problem optimizes the dictionary and the regularizer parameters through supervised learning. The process is carried out via implicit differentiation and gradient-based optimization. We evaluate our method for denoising, super-resolution, and compressed-sensing magnetic-resonance imaging. We compare it to other classical models as well as deep-learning-based methods and show that it always outperforms the former and also the latter in some instances.
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