Magnetic resonance image reconstruction using 2D autoregressive moving average model

Abstract

Discrete Fourier Transform (DFT) is a method of choice for reconstructing Magnetic Resonance Images. It is used as basis for reconstructing images in all types of Data Acquisition techniques ranging from conventional techniques such as Projection Method to the latest Parallel Imaging Techniques. Despite the great success of DFT as reconstruction algorithm, it has some inherit limitation. When used with truncated data, it clearly exhibits artifacts. The data set for DFT is expected to be huge, while practically data acquired are small. DFT works best on smooth image function, while practically MRI data set consists of discrete data set. Application of FT on this data leads to artifacts such as truncation artifacts, spikes at discontinuity point of spectrum (Gibbs Ringging). Although spikes could be flatten by applying windows or filters, but this leads to additional problems such as tiny important pathological images could be suppressed as well. To overcome some of these limitations, few alternatives were proposed such as Modified Backprojection Method (MBM), Parametric Methods (PM), Neural Network Methods (NN), Wavelets Methods (WM), etc. Though, clear reconstructed images can be obtained with NN and WM, however, their data representation is doubtful. Studies show during processing several images with motion and a small tumor, NN and WM successfully reconstructed clear images without any indication of motions has taken place. Yet, the pathological tumor has been averaged away as well. Such clinically these methods are invalid and it is a clear indicative of failure. Parametric methods such as Autoregressive (AR) and Autoregressive Moving Average (ARMA) model give positive result. Research and studies conducted during 1980s and 1990s, clearly showing that ARMA can be a good replacement, but due to the computational complexity, it has not been practically implemented and need further clinical testing. Although there are many algorithms available to solve for ARMA, particularly, Transient Error Reconstruction Approach (TERA) were proven be successful. Taking advantage of current microprocessor speeds and successful implementation of previous variety forms of ARMA algorithms, this research tends to implement 2D ARMA on MRI Data set to reconstruct the images. Modified Transient Error Reconstruction Approach (mTERA) method is proposed to solve for 2D ARMA model. Model orders are proposed to be computed dynamically rather than a fixed value as in TERA method. Different approach of AR parameter determination and final image calculation is also been proposed in comparison with TERA method. Raw data for simulation of 2D m-TERA are obtained from Hospital HTAA, Kuantan with courtesy of Philip® Medical System. Images were reconstructed with proposed algorithm using Matlab®. Finally, reconstructed images from 2D m-TERA are compared with standard method 2D IFFT and performance analysis in term of resolution and reconstruction time is presented.