A Study Of Dictionary Learning In Sparse Representation

In recent years, sparse coding and dictionary learning have been successfully applied to a variety of problems in computer vision and image analysis, including image denoising, image super-resolution, face recognition, as well as higher level tasks such as image classification. This is mainly due to the fact that many natural high-dimensional signals belonging to the same class tend to lie in the same low-dimensional subspace, then a signal can be well approximated by a linear combination of a few atoms from an over-complete dictionary. The performance of sparse coding relies on the quality of dictionary,and many experiments have shown that the learned dictionaries which contain the semantic meaning from the given signals significantly outperform the predefined ones such as discrete cosine transform(DCT), discrete Fourier transform(DFT) and wavelets. So learning an adaptive dictionary is very important. Based on the further study of the existing dictionary learning model, the main contributions are as follows:(1) We present an approach to learn a single dictionary for all different classes of the training samples. The learned dictionary maintains independence between different classes, and it also has a structured feature. The learned dictionary encourages the samples from the same class to have similar sparse codes, and the samples from different classes to have dissimilar sparse codes. The learned classifier makes the classification more easily compared with other methods, especially when the number of classes is very large.(2) For large-scale and dynamic training set, we put forward a semi-supervision online dictionary learning algorithm. According to the gradient approximation principle, the algorithm's convergence is guaranteed, at the same time the use of computer memory is reduced.