The ultrasound carotid images affected by speckle noise, which highly reduces the image quality and effects the human interpretation. Speckle removal is substantial and critical step for preprocessing of ultrasound carotid images. For robust diagnosis, the carotid images must be free of noise and clear in clinical practices. The carotid ultrasound images have multiplicative noise and is very difficult to remove as compared to additive noise. To address this issue we propose to use Bayesian least square estimation in the logarithmic space. The proposed algorithm is tested on 50 ultrasound B mode carotid images and the performance of the algorithm is compared with the existing algorithms like Median filter, Speckle Reducing Anisotropic Diffusion(SRAD), Non Local Mean (NLM) filter, Total Variation (TV), Detail Preserving Anisotropic Diffusion(DPAD) filter, Lee filter, Frost filter and Wavelet filter. Experimental result shows that proposed algorithm capable of achieving better results as compared to the other methods in terms of signal to noise ratio (SNR), peak signal to noise ratio (PSNR), Correlation of Coefficient (CoC), Structural Similarity Index Map (SSIM) and Image Quality Index(IQI) measures. As per visual inspection concerned the proposed approach is more effective in terms of suppression of noise and image enhancement.