Once the i-vector paradigm has been introduced in the field of speaker recognition, many techniques have been proposed to deal with additive noise within this framework. Due to the complexity of its effect in the i-vector space, a lot of effort has been put into dealing with noise in other domains (speech enhancement, feature compensation, robust i-vector extraction and robust scoring). As far as we know, there was no serious attempt to handle the noise problem directly in the i-vector space without relying on data distributions computed on a prior domain. The aim of this paper is twofold. First, it proposes a fullcovariance Gaussian modeling of the clean i-vectors and noise distribution in the i-vector space and introduces a technique to estimate a clean i-vector given the noisy version and the noise density function using the MAP approach. Based on NIST data, we show that it is possible to improve by up to 60% the baseline system performance. Second, in order to make this algorithm usable in a real application and reduce the computational time needed by i-MAP, we propose an extension that requires building a noise distribution database in the i-vector space in an off-line step and using it later in the test phase. We show that it is possible to achieve comparable results using this approach (up to 57% of relative EER improvement) with a sufficiently large noise distribution database.