Among the representation learning, the low-rank representation (LRR) is one of the hot research topics in many fields, especially in image processing and pattern recognition. Although LRR can capture the global structure, the ability of local structure preservation is limited because LRR lacks dictionary learning. In this paper, we propose a novel multi-focus image fusion method based on dictionary learning and LRR to get a better performance in both global and local structure. Firstly, the source images are divided into several patches by sliding window technique. Then, the patches are classified according to the Histogram of Oriented Gradient (HOG) features. And the sub-dictionaries of each class are learned by K-singular value decomposition (K-SVD) algorithm. Secondly, a global dictionary is constructed by combining these sub-dictionaries. Then, we use the global dictionary in LRR to obtain the LRR coefficients vector for each patch. Finally, the (l_1-norm ) and choose-max fuse strategy for each coefficients vector is adopted to reconstruct fused image from the fused LRR coefficients and the global dictionary. Experimental results demonstrate that the proposed method can obtain state-of-the-art performance in both qualitative and quantitative evaluations compared with serval classical methods and novel methods.
The dictionary learning and LRR theory are two major parts in our fusion method. The LRR theory insures that we could capture the global structure of input data. And the dictionary learning processing insures the local structure information could be captured accurately. The K-singular value algorithm (K-SVD) @cite_14 is a standard unsupervised dictionary learning algorithm which is widely investigated in many fields. In this paper, the K-SVD algorithm is used to learn the dictionary. The LRR theory is an important representation learning method. In reference @cite_9 , authors apply self-expression model to avoid training a dictionary and the LRR problem will be solved by the following optimization problem, where @math denotes the observed data matrix, @math denotes the nuclear norm which is the sum of the singular values of matrix. @math is called as @math , @math is the balance coefficient. Eq. is solved by the inexact Augmented Lagrange Multiplier (ALM). Finally, the LRR coefficients matrix @math for @math is obtained by Eq..
@cite_9 @cite_14
79405465 2160547390
We propose low-rank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowest-rank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary. Unlike the well-known sparse representation (SR), which computes the sparsest representation of each data vector individually, LRR aims at finding the lowest-rank representation of a collection of vectors jointly. LRR better captures the global structure of data, giving a more effective tool for robust subspace segmentation from corrupted data. Both theoretical and experimental results show that LRR is a promising tool for subspace segmentation. In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The K-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data