  We address the problem of blind gain and phase calibration of a sensor array
from ambient noise. The key motivation is to ease the calibration process by
avoiding a complex procedure setup. We show that computing the sample
covariance matrix in a diffuse field is sufficient to recover the complex
gains. To do so, we formulate a non-convex least-square problem based on sample
and model covariances. We propose to obtain a solution by low-rank matrix
approximation, and two efficient proximal algorithms are derived accordingly.
The first one solves the problem modified with a convex relaxation to guarantee
that the solution is a global minimizer, and the second one directly solves the
initial non-convex problem. We investigate the efficiency of the proposed
algorithms by both numerical and experimental results according to different
sensing configurations. These show that efficient calibration highly depends on
how the measurements are correlated. That is, estimation is achieved more
accurately when the field is spatially over-sampled.
