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 algorithm solves the problem modified with a convex relaxation to guarantee that the solution is a global minimizer, and the second algorithm directly solves the initial non-convex problem. We investigate the efficiency of the proposed algorithms by numerical and experimental results according to different sensing configurations. These results 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.