Learning Structured Filters For Tensor Convolutional Sparse Coding And Its Applications

As an important data representation method,convolutional sparse coding represents the signal as a sum of convolutions of a set of filters and corresponding sparse coefficients.It has gained wide attention in the fields of computer vision,image processing,and machine learning.In the era of big data,data increasingly presents the characteristics of large-scale and multi-dimensional,such as multi-spectral images and videos.Vector based convolutional sparse coding usually destroys the spatial structure of the data,and has a very large amount of calculation and memory requirements,which leads to its limitation in multi-dimensional data processing.Tensors are a multi-dimensional generalization of vectors and matrices,which could preserve the spatial structure information of data.They have begun to play a central role in various fields,including convolutional sparse coding.In practical problems,the data may potentially have a low multilinear rank structure,which is also widely considered in many tensor methods for data processing,and achieved better results.To improve the performance of convolutional sparse coding in multi-dimensional data processing,this thesis adopts tensor representation to preserve the spatial structure of the data,and introduces structural constraints to the filters.The main results are as follows.1.Two tensor convolutional sparse coding models with structural constraints are proposed.One introduces a low multilinear rank constraint on the filter,and the other represents the filter as a linear combination of some low multilinear rank filters.With the tensor representation,our model could make better use of the spatial structure information of multi-dimensional data.On the other hand,by introducing low multilinear rank structure,the computational complexity of multi-dimensional convolution is significantly reduced.2.Three algorithms are proposed to solve the proposed models.Since the proposed model is non-convex,two of the algorithms use an iterative alternate optimization framework,mainly using ADMM and proximal gradient descent.The third is an approximate algorithm based on the Tucker decomposition.Its computational complexity is lower than the previous two,which also gives a connection between the two proposed models.3.We apply the proposed method to tubular structure segmentation in medical images.Comparative experiments and analysis are carried out on the Olfactory Projection Fibers dataset from the DIADEM challenge.The results show that our method can reduce the time cost without reducing or even improving the segmentation performance.This also shows that the introduction of structural constraints into the tensor convolution sparse coding could improve its usability and thus have a wider range of applications.