Noise reduction in MR echo planar image reconstruction

It is shown that the noise level in EPI (echo planar imaging) can increase very significantly if the final image is deconvolved to remove the ghost artifacts. This noise amplification is caused by divisions of small numbers, which scale the noise variance up. The scaling factor is a function of the frequency variable in the uniform sampling direction, and is small for low-frequency components and large for high-frequency components. A window function to provide an inverse scaling of data so that the noise scaling factor is canceled exactly is proposed. Since the signal energy is concentrated in the low-frequency range, it is not reduced significantly when windowing is applied. The window function is compared to the commonly used Hamming window and is shown to have good frequency response. The algorithm has been tested with computer simulations and has been verified to be able to raise the signal-to-noise ratio by 50% in the final image