Speckle noise of ultrasound images is of multiplicative nature which degrades the image quality in terms of resolution and contrast. While there exist a number of algorithms for reduction of multiplicative Rayleigh distributed random speckle noise, the low signal-to-noise ratio (SNR) issue of the multiplicative Rayleigh noise is still not adequately resolved. In this paper, a simple 2-dimensional (2D) local intensity smoothing method is presented which transforms the Rayleigh noise contaminated in ultrasound images to Nakagami distributed noise so as to improve the SNR of processed images. A 2D total variation regularized Nakagami speckle reduction algorithm is derived based on the maximum a posteriori estimation framework, which performs well in restoring piecewise-smooth reflectivity and preserving fine details of the image. The proposed algorithm is verified by a series of computer-simulated and real ultrasound image data. It is shown that the algorithm considerably improves the quality of ultrasound images and outperforms the Rayleigh noise based speckle reduction methods in terms of speckle SNR and contrast-to-noise ratio.