Image Denoising with Adaptive Weighted Graph Filtering

Graph filtering,which is founded on the theory of graph signal processing,is proved as a useful tool for image denoising.Most graph filtering methods focus on learning an ideal lowpass filter to remove noise,where clean images are restored from noisy ones by retaining the image components in low graph frequency bands.However,this lowpass filter has limited ability to separate the low-frequency noise from clean images such that it makes the denoising procedure less effective.To address this issue,we propose an adaptive weighted graph filtering(AWGF)method to replace the design of traditional ideal lowpass filter.In detail,we reassess the existing low-rank denoising method with adaptive regularizer learning(ARLLR)from the view of graph filtering.A shrinkage approach subsequently is presented on the graph frequency domain,where the components of noisy image are adaptively decreased in each band by calculating their component significances.As a result,it makes the proposed graph filtering more explainable and suitable for denoising.Meanwhile,we demonstrate a graph filter under the constraint of subspace representation is employed in the ARLLR method.Therefore,ARLLR can be treated as a special form of graph filtering.It not only enriches the theory of graph filtering,but also builds a bridge from the low-rank methods to the graph filtering methods.In the experiments,we perform the AWGF method with a graph filter generated by the classical graph Laplacian matrix.The results show our method can achieve a comparable denoising performance with several state-of-the-art denoising methods.

Guided Intra-Patch Smoothing Graph Filtering for Single-Image Denoising

Graph filtering is an important part of graph signal processing and a useful tool for image denoising.Existing graph filtering methods,such as adaptive weighted graph filtering(AWGF),focus on coefficient shrinkage strategies in a graph-frequency domain.However,they seldom consider the image attributes in their graph-filtering procedure.Consequently,the denoising performance of graph filtering is barely comparable with that of other state-of-the-art denoising methods.To fully exploit the image attributes,we propose a guided intra-patch smoothing AWGF(AWGF-GPS)method for single-image denoising.Unlike AWGF,which employs graph topology on patches,AWGF-GPS learns the topology of superpixels by introducing the pixel smoothing attribute of a patch.This operation forces the restored pixels to smoothly evolve in local areas,where both intra-and inter-patch relationships of the image are utilized during patch restoration.Meanwhile,a guided-patch regularizer is incorporated into AWGF-GPS.The guided patch is obtained in advance using a maximum-a-posteriori probability estimator.Because the guided patch is considered as a sketch of a denoised patch,AWGF-GPS can effectively supervise patch restoration during graph filtering to increase the reliability of the denoised patch.Experiments demonstrate that the AWGF-GPS method suitably rebuilds denoising images.It outperforms most state-of-the-art single-image denoising methods and is competitive with certain deep-learning methods.In particular,it has the advantage of managing images with significant noise.

Region-aware neural graph collaborative filtering for personalized recommendation

Personalized recommender systems have been widely deployed in various scenarios to enhance user experience in response to the challenge of information explosion.Especially,personalized recommendation models based on graph structure have advanced greatly in predicting user preferences.However,geographical region entities that reflect the geographical context of the items is not being utilized in previous works,leaving room for the improvement of personalized recommendation.This study proposes a region-aware neural graph collaborative filtering(RA-NGCF)model,which introduces the geographical regions for improving the prediction of user preference.The approach first characterizes the relationships between items and users with a user-item-region graph.And,a neural network model for the region-aware graph is derived to capture the higher-order interaction among users,items,and regions.Finally,the model fuses region and item vectors to infer user preferences.Experiments on real-world dataset results show that introducing region entities improves the accuracy of personalized recommendations.This study provides a new approach for optimizing personalized recommendation as well as a methodological reference for facilitating geographical regions for optimizing spatial applications.