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Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in image processing , signal processing , machine learning , medical imaging , and more.
In applied mathematics, k-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. k-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data.
It also has properties that are useful for signal denoising since usually one can learn a dictionary to represent the meaningful part of the input signal in a sparse way but the noise in the input will have a much less sparse representation. [14] Sparse dictionary learning has been successfully applied to various image, video and audio ...
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. [1] There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of ...
The work by Boyd et al. [16] has applied the LASSO model- for selection of sparse models- towards analog to digital converters (the current ones use a sampling rate higher than the Nyquist rate along with the quantized Shannon representation). This would involve a parallel architecture in which the polarity of the analog signal changes at a ...
Similarly, such a constraint can be applied to its representation itself, generating a cascade of sparse representations: Each code is defined by a few atoms of a given set of convolutional dictionaries. Based on these criteria, yet another extension denominated multi-layer convolutional sparse coding (ML-CSC) is proposed.
Matching pursuit has been applied to signal, image [2] and video coding, [3] [4] shape representation and recognition, [5] 3D objects coding, [6] and in interdisciplinary applications like structural health monitoring. [7]
Sparse matrix representations only store non-zero matrix entries and implicitly represent the zero entries. They can, for example, be used to represent sparse graphs without incurring the space overhead from storing the many zero entries in the adjacency matrix of the sparse graph.