The quest of `can machines think' and `can machines do what human do' are quests that drive the development of artificial intelligence. Although recent artificial intelligence succeeds in many data intensive applications, it still lacks the ability of learning from limited exemplars and fast generalizing to new tasks. To tackle this problem, one has to turn to machine learning, which supports the scientific study of artificial intelligence. Particularly, a machine learning problem called Few-Shot Learning (FSL) targets at this case. It can rapidly generalize to new tasks of limited supervised experience by turning to prior knowledge, which mimics human's ability to acquire knowledge from few examples through generalization and analogy. It has been seen as a test-bed for real artificial intelligence, a way to reduce laborious data gathering and computationally costly training, and antidote for rare cases learning. With extensive works on FSL emerging, we give a comprehensive survey for it. We first give the formal definition for FSL. Then we point out the core issues of FSL, which turns the problem from "how to solve FSL" to "how to deal with the core issues". Accordingly, existing works from the birth of FSL to the most recent published ones are categorized in a unified taxonomy, with thorough discussion of the pros and cons for different categories. Finally, we envision possible future directions for FSL in terms of problem setup, techniques, applications and theory, hoping to provide insights to both beginners and experienced researchers.

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.