We analyze the Basis Pursuit recovery of signals with general perturbations.
Previous studies have only considered partially perturbed observations Ax + e.
Here, x is a signal which we wish to recover, A is a full-rank matrix with more
columns than rows, and e is simple additive noise. Our model also incorporates
perturbations E to the matrix A which result in multiplicative noise. This
completely perturbed framework extends the prior work of Candes, Romberg and
Tao on stable signal recovery from incomplete and inaccurate measurements. Our
results show that, under suitable conditions, the stability of the recovered
signal is limited by the noise level in the observation. Moreover, this
accuracy is within a constant multiple of the best-case reconstruction using
the technique of least squares. In the absence of additive noise numerical
simulations essentially confirm that this error is a linear function of the
relative perturbation.

分析基 Pursuit 信号恢复中的波动干扰，即数学模型中的加性噪声与乘性噪声，结果显示在合适的条件下，恢复信号的稳定性受观测噪声水平的限制，同时，在无加性噪声的情况下，恢复的误差是相对扰动的线性函数，并且准确性与最小二乘技术的最佳重建处于常数倍数的范围内。