Multivariate Fields of Experts
This work addresses image reconstruction tasks like denoising and deblurring for researchers and practitioners, offering an incremental improvement over existing fields of experts methods.
The authors tackled the problem of learning image priors for inverse problems by introducing multivariate fields of experts, which generalize existing methods with multivariate potential functions based on Moreau envelopes of the ℓ∞-norm. The result showed that this approach outperforms comparable univariate models, achieves performance close to deep-learning-based regularizers, and is significantly faster with fewer parameters and training data.
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 relatively high level of interpretability due to its structured design.