General Convolutional Sparse Coding with Unknown Noise
This work addresses the problem of restrictive noise assumptions in CSC for researchers in signal processing and biomedical applications, though it is incremental as it extends existing CSC methods.
The paper tackles the limitation of convolutional sparse coding (CSC) methods that only model Gaussian noise by proposing a general CSC model that handles unknown noise using a Gaussian mixture model, achieving effective noise modeling and high-quality filters and representation in experiments on biomedical data.
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this paper, we propose a general CSC model capable of dealing with complicated unknown noise. The noise is now modeled by Gaussian mixture model, which can approximate any continuous probability density function. We use the expectation-maximization algorithm to solve the problem and design an efficient method for the weighted CSC problem in maximization step. The crux is to speed up the convolution in the frequency domain while keeping the other computation involving weight matrix in the spatial domain. Besides, we simultaneously update the dictionary and codes by nonconvex accelerated proximal gradient algorithm without bringing in extra alternating loops. The resultant method obtains comparable time and space complexity compared with existing CSC methods. Extensive experiments on synthetic and real noisy biomedical data sets validate that our method can model noise effectively and obtain high-quality filters and representation.