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Orthogonal Matching Pursuit (OMP) is an effective solution to sparse approximation based on redundant dictionary, but there are plenty of matrix-vector multiplications in order to seek for the most matching atom. This full search scheme can consume much CPU time, especially for high dimension data such as image. Although some existing schemes proposed some accelerating methods by exploiting the property of atoms in parametric dictionary, they cannot be extended to other dictionaries, especially learned dictionary. Considering statistical nature of atoms in learned dictionary, this paper proposes a novel method which utilizes modified K-mean algorithm to cluster all the atoms in the learned dictionary while sufficiently considering the inner product operation between every two atoms, determines the class in which the desired atom locates and finally find it in the class. Some analyses and experiments have shown the success of the method. In addition, this paper gives some empirical analysis of the effect of related parameters of indexed dictionary. [ABSTRACT FROM AUTHOR]

The goal of this paper is to solve mathematical model equations on solid tumour growth and compute their parameter values by applying growth rates of prostate cancer cell lines in vivo. For these computations, we investigate previously developed C3(1)/Tag transgenic models of prostate cancer. To make the computations fast, we have constructed an algorithm, which is based on small amounts of spatial grid-points and obtained a correspondence between the in vivo growth of tumours and the solutions of the model equations. [ABSTRACT FROM AUTHOR]