Abstract
Conventional deep neural nets (DNNs) initialize network parameters at random and then optimize each one via stochastic gradient descent (SGD), resulting in substantial risk of poor-performing local this http URL on the image interpolation problem and leveraging a recent theorem that maps a (pseudo-)linear interpolator {\Theta} to a directed graph filter that is a solution to a MAP problem regularized with a graph shift variation (GSV) prior, we first initialize a directed graph adjacency matrix A based on a known interpolator {\Theta}, establishing a baseline this http URL, towards further gain, we learn perturbation matrices P and P(2) from data to augment A, whose restoration effects are implemented via Douglas-Rachford (DR) iterations, which we unroll into a lightweight interpretable neural this http URL results demonstrate state-of-the-art image interpolation results, while drastically reducing network parameters.
Abstract (translated)
传统的深度神经网络（DNN）在网络参数初始化时采用随机方式，然后通过随机梯度下降（SGD）优化每个参数，这会导致陷入次优局部极小值的风险。本文针对图像插值问题，并利用最近的一个定理，该定理将一个线性或伪线性插值器{\Theta}映射为带有图移变差（GSV）先验的极大似然估计（MAP）问题的解所对应的有向图滤波器。首先，我们基于已知的插值器{\Theta}初始化了一个有向图邻接矩阵A，以此建立一个基准点。 为了进一步提高性能，我们从数据中学习到扰动矩阵P和P(2)，用以增强矩阵A，其恢复效果通过道格拉斯-拉奇福德（DR）迭代来实现，并将其展开成轻量级可解释的神经网络。实验结果表明，在大幅减少网络参数的同时，达到了最先进的图像插值性能。
URL
https://arxiv.org/abs/2509.11926
