In this paper, we propose a novel robust method for short-time spectral amplitude (STSA) estimation in audio denoising. This method extends the smoothed sigmoid-based shrinkage (SSBS), which does not require any prior information about the probability distribution of the signal of interest. With regard to audio processing, the SSBS method yields better performance in terms of noise reduction but nevertheless introduces significant musical noise. In order to benefit from non-diagonal processing, which removes background noise without introducing musical noise, two non-diagonal SSBS are derived. First, the decision directed approach is incorporated into the SSBS method. Second, the time-frequency domain is divided into rectangular blocks and then, a SSBS function is applied to estimate the spectral amplitude in each block. The experimental results demonstrate the relevance of the proposed methods both in terms of speech quality and intelligibility via objective criteria.