This document proposes an adaptive noise driven total variation filtering method for denoising magnitude MR images corrupted by Rician noise. It begins with an introduction to MR imaging and Rician noise in magnitude MR images. Existing denoising methods like Gaussian, wavelet and total variation filtering are discussed. The proposed method estimates the noise level using local variances and adapts the regularization parameter in total variation filtering accordingly. Experimental results show the proposed method achieves better denoising performance than non-local means, bilateral and multiscale LMMSE filtering based on mean opinion scores and metrics like MSE and SSIM.