Fast Subspace Tracking Algorithm

Compressive sensing is a novel signal sampling theory under the condition that the signal is sparse or compressible. It has the ability of compressing a signal during the process of sampling. Reconstruction algorithm is the key part besides of sensing matrix in compressive sensing, and it is of great significance to accurately reconstruct a signal and verify the sampling accuracy. In this paper, properties of the existing reconstruction algorithms are firstly analyzed.Firstly,we introduce a new method for reconstruction of sparse signals, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity and high reconstruction accuracy. In the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter. The mean squared error of the reconstruction is upper bounded by constant multiples of the measurement and signal perturbation energies.Secondly, a fast subspace pursuit algorithm is proposed to reconstruct sparse signals for compressive sensing. In order to reduce the computational cost, we symbolize the sampling matrix. As the result, multiplication is not required in the step of calculating the correlation. The analysis and simulation results reveal that the computational complexity of the proposed algorithm is much lower than that of the original subspace pursuit algorithm whereas the performance loss is fairly acceptable.Finally, stuty of application of gene profile classification make use of compressive sensing technologe is produced. Gene profile classification is to find out the sparse representation of testing samples with training samples.Fast subspace pursuit is much more efficient than other sparse representation methods. The compressive sensing approach has the performance which can match the best result achieved among all the SVM variants after careful model selection.