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This paper tackles the problem of reducing the speckle noise in the ultrasound B-Scan image while preserving the structure of boundaries and lesions. Our contribution is two fold. (1) We demonstrate for the first time that ICA Sparse Code Shrinkage (ICA-SCS) denoising algorithm can be applied to the envelope-detected ultrasound B-Scan image despeckling problem. ICA-SCS denoising algorithm is successful when the noise is additive white Gaussian noise (WGN). It uses higher order statistics and is also data adaptive. However, the speckle noise found in medical ultrasound B-Scan image is not strictly additive WGN. (2) Therefore, as a secondary improvement, we have incorporated a preprocessing step, developed by others, that makes the speckle noise much closer to the real additive WGN, hence more amenable to a denoising algorithm such as ICA-SCS. The experimental results show that the proposed method outperforms several classical methods chosen for comparison such as Wiener filtering and wavelet shrinkage, in its ability to reduce speckle and preserve edge details.