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
1963932623 2088254198 2084716923 2101350717
A label consistent K-SVD (LC-KSVD) algorithm to learn a discriminative dictionary for sparse coding is presented. In addition to using class labels of training data, we also associate label information with each dictionary item (columns of the dictionary matrix) to enforce discriminability in sparse codes during the dictionary learning process. More specifically, we introduce a new label consistency constraint called "discriminative sparse-code error" and combine it with the reconstruction error and the classification error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. Our algorithm learns a single overcomplete dictionary and an optimal linear classifier jointly. The incremental dictionary learning algorithm is presented for the situation of limited memory resources. It yields dictionaries so that feature points with the same class labels have similar sparse codes. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse-coding techniques for face, action, scene, and object category recognition under the same learning conditions. In this paper, we propose a novel coupled dictionary training method for single-image super-resolution (SR) based on patchwise sparse recovery, where the learned couple dictionaries relate the low- and high-resolution (HR) image patch spaces via sparse representation. The learning process enforces that the sparse representation of a low-resolution (LR) image patch in terms of the LR dictionary can well reconstruct its underlying HR image patch with the dictionary in the high-resolution image patch space. We model the learning problem as a bilevel optimization problem, where the optimization includes an l1-norm minimization problem in its constraints. Implicit differentiation is employed to calculate the desired gradient for stochastic gradient descent. We demonstrate that our coupled dictionary learning method can outperform the existing joint dictionary training method both quantitatively and qualitatively. Furthermore, for real applications, we speed up the algorithm approximately 10 times by learning a neural network model for fast sparse inference and selectively processing only those visually salient regions. Extensive experimental comparisons with state-of-the-art SR algorithms validate the effectiveness of our proposed approach. A label consistent K-SVD (LC-KSVD) algorithm to learn a discriminative dictionary for sparse coding is presented. In addition to using class labels of training data, we also associate label information with each dictionary item (columns of the dictionary matrix) to enforce discriminability in sparse codes during the dictionary learning process. More specifically, we introduce a new label consistent constraint called ‘discriminative sparse-code error’ and combine it with the reconstruction error and the classification error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. Our algorithm learns a single over-complete dictionary and an optimal linear classifier jointly. It yields dictionaries so that feature points with the same class labels have similar sparse codes. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse coding techniques for face and object category recognition under the same learning conditions. Dictionary learning has became an increasingly important task in machine learning, as it is fundamental to the representation problem. A number of emerging techniques specifically include a codebook learning step, in which a critical knowledge abstraction process is carried out. Existing approaches in dictionary (codebook) learning are either generative (unsupervised e.g. k-means) or discriminative (supervised e.g. extremely randomized forests). In this paper, we propose a multiple instance learning (MIL) strategy (along the line of weakly supervised learning) for dictionary learning. Each code is represented by a classifier, such as a linear SVM, which naturally performs metric fusion for multi-channel features. We design a formulation to simultaneously learn mixtures of codes by maximizing classification margins in MIL. State-of-the-art results are observed in image classification benchmarks based on the learned codebooks, which observe both compactness and effectiveness.