SVD singular value decomposition derivation and application and signal recovery

1、 application ：SVD For signal estimation
Such as ： From the signal Y Recover the signal z And x,( among W It is complex Gaussian white noise ）

2、 The following is derived ： The matrix A Singular value decomposition ：

3、 therefore ： Through singular value decomposition , The signal can be estimated z And x, Among them, the estimated z And x Is the first column vector taken （ guess ： Because singular value lamda It is arranged from large to small , The largest singular value can represent the largest feature of the signal ）

4、 reference ：

Kalman D . A Singularly Valuable Decomposition: The SVD of a Matrix[J]. The College Mathematics Journal, 1996, 27(1):2-23.