We introduce the multivariate fields of experts, a new framework for the learning of image priors. Our model generalizes existing fields of experts methods by incorporating multivariate potential functions constructed via Moreau envelopes of the $\ell_\infty$-norm. We demonstrate the effectiveness of our proposal across a range of inverse problems that include image denoising, deblurring, compressed-sensing magnetic-resonance imaging, and computed tomography. The proposed approach outperforms comparable univariate models and achieves performance close to that of deep-learning-based regularizers while being significantly faster, requiring fewer parameters, and being trained on substantially fewer data. In addition, our model retains a high level of interpretability due to its structured design. It is supported by theoretical convergence guarantees which ensure reliability in sensitive reconstruction tasks.

翻译：本文提出了多元专家场，一种用于学习图像先验的新框架。我们的模型通过引入基于$\ell_\infty$范数莫罗包络构建的多元势函数，推广了现有的专家场方法。我们在包括图像去噪、去模糊、压缩感知磁共振成像和计算机断层扫描在内的一系列逆问题上验证了所提方法的有效性。该方法优于可比较的单变量模型，其性能接近基于深度学习的正则化方法，同时具有显著更快的计算速度、更少的参数需求，且训练所需数据量大幅减少。此外，由于采用结构化设计，我们的模型保持了较高的可解释性。理论收敛性保证为该模型提供了支撑，确保了在敏感重建任务中的可靠性。