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This paper presents a novel maximum a posteriori (MAP) denoising algorithm based on the independent component analysis (ICA). We demonstrate that the employment of individual ICA transformations for signal and noise can provide the best estimate within the linear framework. The signal enhancement problem is categorized based on the distribution of signal and noise being Gaussian or non-Gaussian and the estimation rule is derived for each of the categories. Our theoretical analysis shows that under the assumption of a Gaussian noise the proposed algorithm leads to some well-known enhancement techniques, i.e., Wiener filter and sparse code shrinkage. The analysis of the denoising capability shows that the proposed algorithm is most efficient for non-Gaussian signals corrupted by a non-Gaussian noise. We employed the generalized Gaussian model (GGM) to model the distributions of speech and noise. Experimental evaluation is performed in terms of signal-to-noise ratio (SNR) and spectral distortion measure. Experimental results show that the proposed algorithms achieve significant improvement on the enhancement performance in both Gaussian and non-Gaussian noise.