Existing multichannel blind restoration techniques are prone to noise, assume perfect spatial alignment of channels and a correct estimation of blur size. We develop an alternating minimization scheme based on maximum a posteriori probability estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the total variation semi-norm. This stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise. We observe that the exact knowledge of the blur size is not necessary and we show that translation misregistration up to a certain extent can be automatically removed in the restoration process.