一种用于稀疏表示的原子库设计新方法

n algorithm was proposed for adapting dictionaries to achieve sparse signal representation. Given a set of training signals, we seek a dictionary that leads to the best representation for each member in this set under strict sparsity. Q-Moore Penrose Inverse (Q-MPI) algorithm is also an iterative method that alternates between sparse representation of the training signals based on the current dictionary, and update of the dictionary to better fit the data. Q-MPI algorithm is flexible and can work with any sparse coding method (e.g., Matching pursuit, Orthogonal Matching Pursuit, Basis Pursuit). Different from other algorithms, Q-MPI updates dictionary based on Moore Penrose Inverse. Besides, Q-MPI algorithm divides training samples into a few groups when the amount of it is relatively large. In this way, Q-MPI algorithm could avoid trapping into local optimum and achieve a satisfying result. We compare Q-MPI algorithm to state-of-the-art algorithms, and the results show that Q-MPI algorithm is equivalent or superior to the others. Combining grouping strategies with other dictionary learning methods, they could be improved in some ways. Furthermore, we employ Q-MPI to train a dictionary based on noisy images, then use it to achieve image denoising.