Diffusion PDE-based denoising technique for magnetic resonance electrical impedance tomography

Recent progress in Magnetic Resonance Electrical Impedance Tomography (MREIT) research has shown that conductivity images with higher spatial resolution and accuracy are achievable. One of the most important remaining problems to be solved in MREIT before we can apply the technique to human subjects is how to reduce the amount of injection current. Since we use an MRI scanner to measure the induced magnetic flux density data subject to an injection current, the data is contaminated with random noise. In order to obtain enough signal-to-noise ratio (SNR), we need to inject a large amount of current into the subject. However, it is obvious that we must comply with the electrical safety regulations and this means that we should deal with noisy data having a low SNR due to the limited amount of injection current Furthermore, in the developed reconstruction algorithms, the required numerical differentiations of the noisy data may result in deterioration of the reconstructed conductivity image leading to a loss of important information. In this paper, we propose a PDE-based denoising technique that diminishes the degradation of reconstructed conductivity images due to the noise in measured data. The proposed PDE-based technique is advantageous in reducing the random noise while preserving useful features in MREIT.