Dictionary learning algorithms for sparse representation
Neural Computation
Approximating extent measures of points
Journal of the ACM (JACM)
Sublinear-time approximation algorithms for clustering via random sampling
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Bi-criteria linear-time approximations for generalized k-mean/median/center
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
An effective coreset compression algorithm for large scale sensor networks
Proceedings of the 11th international conference on Information Processing in Sensor Networks
Compressive light field photography using overcomplete dictionaries and optimized projections
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Signal and image processing have seen in the last few years an explosion of interest in a new form of signal/image characterization via the concept of sparsity with respect to a dictionary. An active field of research is dictionary learning: Given a large amount of example signals/images one would like to learn a dictionary with much fewer atoms than examples on one hand, and much more atoms than pixels on the other hand. The dictionary is constructed such that the examples are sparse on that dictionary i.e each image is a linear combination of small number of atoms. This paper suggests a new computational approach to the problem of dictionary learning. We show that smart non-uniform sampling, via the recently introduced method of coresets, achieves excellent results, with controlled deviation from the optimal dictionary. We represent dictionary learning for sparse representation of images as a geometric problem, and illustrate the coreset technique by using it together with the K---SVD method. Our simulations demonstrate gain factor of up to 60 in computational time with the same, and even better, performance. We also demonstrate our ability to perform computations on larger patches and high-definition images, where the traditional approach breaks down.