英文-压缩感知理论及OMP算法.ppt

2011-01-25 An Overview of Compressive Sensing For 1-D signal X∈RN×1, mostly，the information is redundant. 。 We can compress it by orthogonal transformation. An Overview of Compressive Sensing But there are some flaws of this method: 1) Considering the Shannon sampling theorem，the sampling interval will be very narrow to gain better signal resolution，which will make the original signal very long, so the processing of transformation costs lots of time. 2) The positions of K components required to remain vary while the signal changes. Therefore, this strategy is self-adaptive, and we need to allocate more space to store these positions. 3) Poor anti-interference. Once one of the K components lost in transmission, the output will be changed greatly. An Overview of Compressive Sensing In 2004, Donoho and Candes put forward the theory of compressive sensing. This theory indicates that when the signal is sparse or compressible, the signal can be reconstructed accurately or approximately by gathering very few projective values of the signal. An Overview of Compressive Sensing The advantages of compressive sensing: 1) Non-adaptive, break through the limitation of Shannon sampling theorem. 2) Strong Anti-interference ability, every component of the measurement is important, or unimportant. It can still be reconstructed while some components are lost. The application prospect of compressive sensing is broad: digital camera and audio acquisition device with low cost; astronomy (stars are sparse); network; military. An Overview of Compressive Sensing Suppose x (n) is a digital signal, if it’s a K-sparse (has K non-zero values) or compressible signal, then we can estimate it with few coefficients by linear transformation. By compressive sensing we get the signal y (m) (mn), y=Φx Φ is called sensing matrix with m×n dimension. The dimension of y is much less than that of x, so the equation has infinitive solutions, which makes it difficult to rebuild original signal. Since