Abstract
Sparse representations classification (SRC) is a powerful technique for pixelwise classification of images and it is increasingly being used for a wide variety of image analysis tasks. The method uses sparse representation and learned redundant dictionaries to classify image pixels. In this empirical study we propose to further leverage the redundancy of the learned dictionaries to achieve a more accurate classifier. In conventional SRC, each image pixel is associated with a small patch surrounding it. Using these patches, a dictionary is trained for each class in a supervised fashion. Commonly, redundant/overcomplete dictionaries are trained and image patches are sparsely represented by a linear combination of only a few of the dictionary elements. Given a set of trained dictionaries, a new patch is sparse coded using each of them, and subsequently assigned to the class whose dictionary yields the minimum residual energy. We propose a generalization of this scheme. The method, which we call multiple sparse representations classification (mSRC), is based on the observation that an overcomplete, class specific dictionary is capable of generating multiple accurate and independent estimates of a patch belonging to the class. So instead of finding a single sparse representation of a patch for each dictionary, we find multiple, and the corresponding residual energies provides an enhanced statistic which is used to improve classification. We demonstrate the efficacy of mSRC for three example applications: pixelwise classification of texture images, lumen segmentation in carotid artery magnetic resonance imaging (MRI), and bifurcation point detection in carotid artery MRI. We compare our method with conventional SRC, K-nearest neighbor, and support vector machine classifiers. The results show that mSRC outperforms SRC and the other reference methods. In addition, we present an extensive evaluation of the effect of the main mSRC parameters: patch size, dictionary size, and sparsity level.
Highlights
The use of learned, overcomplete dictionaries and sparse representations of signals has been shown to yield state-of-the-art performance in reconstructive image processing tasks [1,2,3,4], PLOS ONE | DOI:10.1371/journal.pone.0131968 July 15, 2015collection and analysis, decision to publish, or preparation of the manuscript
An exception is the results obtained with a sparsity level of 1: after an initial improvement in performance when using 2–4 sparse representations, a small but consistent decay is seen for higher numbers of sparse representations
Another exception to the positive effect of multiple sparse representations classification (mSRC) is seen in the top-left and mid-left plots, for sparsity levels of 9
Summary
Dictionary LearningThere are several ways to learn a dictionary [24]. Here we have adopted the K-SVD algorithm [25], which is a relatively efficient method that incorporates the sparsity prior in the training process. . .xM] be a matrix of L2-normalized training signals xi 2 Rn. Let X = [x1x2. . .xM] be a matrix of L2-normalized training signals xi 2 Rn In this study, the latter are vectorized image patches describing the local neighborhood around the voxel in the patch center, where the size of the patches is chosen such that they capture the structures that are relevant for the task at hand. K-SVD, approximates the solution by alternating between a greedy sparse coding step using the current dictionary estimate, and a dictionary update step. This has been shown to converge to a dictionary that is very close to the optimal one [26]
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