Theory And Applications Of Shearlet Scattering Transform

A central problem in signal processing and computer vision is to produce good representations of data.Convolutional neural networks have achieved significant success in this area,but its underlying mechanisms are not well understood.Recently,the understanding of convolutional neural networks has received more and more attention.The wavelet scattering transform is a pioneering work on this topic.It can be proved that it has the properties of translation invariance and deformation stability.However,in terms of image representation,a shortcoming is the lack of directional selectivity and sparsity.Therefore,when there are anisotropic structures such as rich edges in the image,its application has some limitations.To overcome this problem,a new multiscale geometric analysis tool,shearlets,is a good choice.Not only does it have the ability to capture anisotropic structures in an image,but it also provides a nearly optimal sparse approximation to the image.Moreover,it offers the benefit of a consistent treatment for discrete implementation and continuous domain theory.Therefore,this dissertation proposes the shearlet scattering transform and studies its properties,and then investigates its fusion with suitable convolutional neural networks and related applications.The main contributions are as follows.1.We propose the shearlet scattering transform.It is a cascade of shearlet transforms and modulus nonlinearities,with a specific convolutional neural network architecture.The locally invariant representations computed for images exhibit significant directional selectivity and sparsity.Furthermore,with the sequence of cone-adapted semi-discrete shearlet systems,the theory of shearlet scattering transforms,including its basic properties and computational methods,is studied.The proposed shearlet scattering transform is nonexpansive,energy-preserving and locally invariant,and the conditions are given theoretically.2.We propose a convolutional neural network,namely WR2N.Based on the wide residual network,to improve the capabilities of learning fine-grained multiscale features,it splits the filters in specific layers into several groups and connects them in a hierarchical residual-like manner.Furthermore,by fusing the shearlet scattering transform and WR2N,we propose a more convenient hybrid complex shearlet scattering network.The idea is to use shearlet scattering transform to encode more prior knowledge,thereby reducing the learning difficulty of data-driven WR2N.3.We apply the proposed hybrid complex shearlet scattering network to COVID-19 detection with chest CT images.Due to the ability to conveniently learn finegrained multiscale features,the extracted features are more discriminative and stable.Extensive experimental results on real world datasets show that the proposed method outperforms several state-of-the-art COVID-19 detection methods.We can achieve higher accuracy,F1-score and AUC,as well as more accurate and refined class activations maps.In particular,the average accuracy improves from 1.08%p to 12.15%p,and the average AUC improves from 1.03%p to 14.39%p.4.We propose a multimodal deep neural network for fake news detection.It builds representative feature extraction subnetworks for two different modalities,namely image and text,respectively.For images,we use the proposed hybrid complex shearlet scattering network to extract fine-grained multiscale features.For text,we propose a graph representation method based on tensor CP decomposition and LSTM,and then employ a graph convolutional network to extract text features.Extensive experiments on real world datasets show that our method outperforms several state-of-the-art methods in terms of accuracy,F1 score,and AUC.In particular,the average accuracy improves from 1.81%p to 10.77%p,and the average AUC improves from 1.74%p to 6.09%p.