The Research Of Dictionary Learning Methods In Sparse Representation And Its Application In Image Classification

The sparse representation has achieved great success in the field of signal representation in recent years. It is widely used in some important application areas, such as pattern recognition, machine learning, computer vision and medical imaging. The effect of Sparse representation is largely depends to the choosing of Dictionary. There are so many kinds of signals, each of them have its own characteristics and structure. The fixed Dictionary can not always suit for the signals, so a Learned Dictionary is needed to achieve a better result. This paper have done some research in dictionary learning and its application in image classification. The specific is summarized as follows:(1) First, We have introduced the Simple mathematical model of the sparse representation. Then we give the detailed description of sparse decomposition problem according to the difference of constraints on sparse coefficients. We also introduced the development of Dictionary and some traditional dictionary learning methods..(2) We give a detail analysis about dictionary learning methods which used in classification tasks. According to the the way how the class labels included into the learning of the dictionary or sparse coefficients, we categorized the dictionary learning method into two different groups:discriminant dictionary learning and Joint Dictionary and Classifier Learning.(3) According to the existed dictionary learning methods, this paper proposed a improved Fisher discriminant dictionary learning method. Experiments on USPS datasets showed that it is faster than FDDL algorithm.(4) Under the sparse representation-based classification framework, we use the improved Fisher discriminant dictionary method combined with Manifold subspace presents a fisher discriminant dictionary learning method for pattern recognition with reject options to solve the problem which the test data do not belong to the training data. In this model, the first thing is to add the fisher discriminant constraint to the objective function of dictionary learning, so that the sparse decomposition coefficients under the learned dictionary could be have a larger scatter between classes and a smaller scatter within one class. Then build several local linear manifold subspace for the coefficients of the training data to make a approximation of the nonlinear manifold space which the coefficients belong to.