Fast denoising techniques for transverse relaxation time estimation in MRI

Estimating the transverse relaxation time (T
₂
) from magnitude spin echo images is a common problem in Magnetic Resonance Imaging. The standard approach is to use pixelwise estimates; however these estimates can be quite noisy when only two images are available. By imposing inter-pixel information the estimates can be improved. An optimal formulation of the problem is nonlinear and typically time consuming to solve. Here we propose two fast methods to reduce the variance of the T
₂
estimates: 1) a simple local least squares (LS) method, and 2) a total variation based approach that can be cast as a linear program. The two approaches are evaluated using both simulated and in vivo data. We show that the variance of the proposed T
₂
estimates is smaller than the pixelwise estimates without compromising tissue contrast.