Study On Sparse Recovery Algorithms And Their Applications To DOA Estimation

To recovery the sampled signals or images, traditional methods require samplingrate obeying Nyquist sampling theory, i.e., sampling rate must be2times at least asthe signal frequency. In recent years, a new kind of theory called CS (compressivesensing/sampling) Theory was proposed, and supported by this theory sparse recoveryalgorithms are increasingly attracting attentions from academic and engineering fields.In the framework of this theory, one can recovery or reconstruct the data sampled as alower rate than Nyquist sampling rate, if some sparse forms are satisfied. The sparseforms can emerge in time domain, frequency domain, space-time domain and so on,and besides, approximate sparsity can be also accepted.Sparse recovery methods contain convex algorithms, greedy algorithms and FO-CUSS algorithms. The principle of convex algorithms is utilizing SOC programmingto approximate the sparse solution. The advantages of convex algorithms are that sam-ples are not needed too many and the result is stable, while the drawback is its highcomputational complexity. Greedy algorithms, containing MP, OMP, CoSaMP and soon, approximate the sparse solution through marching operation between residual er-ror and sampling matrix and cutting basis of the small values in each iteration. Theadvantages of greedy algorithms are low-computation and fast convergent, while thedrawback is that numerous samples are needed. FOCUSS are belong to re-weighted2-form minimum algorithms, with the characters of the small samples needed, lowcomputation and fast convergence. And this article proposed TLS-FOCUSS and SD-FOCUSS under the framework of FOCUSS. Besides, there are others sparse recoveryalgorithms such as IAA-APES, SpaRSA and so on.About sparse recovery, researchers considered only two kind of signal models,that is non-noise model and measurement noise model. However, few works concernsthe sparse problem that the sensing matrix is also perturbed by noise. On above men-tioned problem, TLS-FOCUSS and SD-FOCUSS are proposed based on FOCUSS and TLS methods. The new algorithms are proved to be efcient and practical comparedwith other sparse algorithms through simulations.Due to the excellent performance in the fields of signal processing, informationencoding, medical imaging and so on, sparse recovery have been concerned univer-sally and increasingly. Limited by space of the paper, we apply the sparse recoveryalgorithms just in DOA estimation, then analyze the performance compared with tra-ditional methods of DOA estimation.The innovations of this paper contain:TLS-FOCUSS algorithm；SD-FOCUSS algorithm；The analysis of uncertainty with RIP in DOA estimation using sparse recoveryalgorithms.