UniHIST: A unified framework for image restoration with marginal histogram constraints

Marginal histograms provide valuable information for various computer vision problems. However, current image restoration methods do not fully exploit the potential of marginal histograms, in particular, their role as ensemble constraints on the marginal statistics of the restored image. In this paper, we introduce a new framework, UniHIST, to incorporate marginal histogram constraints into image restoration. The key idea of UniHIST is to minimize the discrepancy between the marginal histograms of the restored image and the reference histograms in pixel or gradient domains using the quadratic Wasserstein (W₂) distance. The W₂ distance can be computed directly from data without resorting to density estimation. It provides a differentiable metric between marginal histograms and allows easy integration with existing image restoration methods. We demonstrate the effectiveness of UniHIST through denoising of pattern images and non-blind deconvolution of natural images. We show that UniHIST enhances restoration performance and leads to visual and quantitative improvements over existing state-of-the-art methods.