Optimal Model Order Selection for Transient Error Autoregressive Moving Average (TERA) MRI Reconstruction Method Abiodun M. Aibinu, Athaur Rahman Najeeb, Momoh J. E. Salami, and Amir A. Shafie Abstract—An alternative approach to the use of Discrete Fourier Transform (DFT) for Magnetic Resonance Imaging (MRI) recon- struction is the use of parametric modeling technique. This method is suitable for problems in which the image can be modeled by explicit known source functions with a few adjustable parameters. Despite the success reported in the use of modeling technique as an alternative MRI reconstruction technique, two important problems constitutes challenges to the applicability of this method, these are estimation of Model order and model coefficient determination. In this paper, five of the suggested method of evaluating the model order have been evaluated, these are: The Final Prediction Error (FPE), Akaike Information Criterion (AIC), Residual Variance (RV), Minimum Description Length (MDL) and Hannan and Quinn (HNQ) criterion. These criteria were evaluated on MRI data sets based on the method of Transient Error Reconstruction Algorithm (TERA). The result for each criterion is compared to result obtained by the use of a fixed order technique and three measures of similarity were evaluated. Result obtained shows that the use of MDL gives the highest measure of similarity to that use by a fixed order technique. Keywords—Autoregressive Moving Average (ARMA), Magnetic Resonance Imaging (MRI), Parametric modeling, Transient Error. I. I NTRODUCTION Magnetic Resonance Imaging (MRI) is used primarily in medical fields to produce images of the internal section of the human body [1]–[3]. The raw data or k-space data obtained, often made up of M x N e.g (256 x 128 ) complex valued data points. These data are reconstructed in order to obtain the final image called MR images. The basic MR reconstruction can be regarded as finding an image function P that is consistent with the measured signal S according to a known imaging equation S = f [P ] (1) where f represent spatial information encoding scheme [1]. Furthermore, If f is invertible, a data consistent P can be obtained from the inverse transform such that P = f -1 S (2) In real life f [S] cannot be computed because of the nature of the data space which is partially sampled, instead of directly Athaur Rahman Najeeb is with the Kulliyah of Engineering, International Islamic University Malaysia (IIUM), email: athaur@iiu.edu.my Momoh.J.E Salami is with the Kulliyah of Engineering, International Islamic University Malaysia (IIUM), email: momoh@iiu.edu.my Amir A. Shafie is with the Kulliyah of Engineering, International Islamic University Malaysia (IIUM), email: aashafie@iiu.edu.my Abiodun. M. Aibinu, Malaysia, email: maibinu@gmail.com implementing the inversion formula, one focuses on finding an image function that satisfy the data consistency constrain [1]. Methods involve in MR reconstruction can broadly be divided into two namely: Non parametric and Parametric methods of MR reconstruction [4]. The use of Non-parametric technique such as the use of a two-dimensional discrete Fourier transform (DFT) as an MRI reconstruction technique has found common usage in the field of MRI. Despite the popularity of this technique,it still suffers from Gibb’s effect, introduction of artifacts and decrease in Spatial resolution. Parametric modeling technique is suitable for problems in which the image can be modeled by explicit known source functions with a few adjustable parameters [7]. In the field of MRI reconstruction, this involves modelling the rows or columns data of the acquired data points or in some cases model both the rows and the columns [1], [2], [4], [6], [8]–[10] as an image reconstruction scheme. The general principles governing the use of modeling techniques for image reconstruction are: • Sufficiency: The model must accurately represent the image. • Efficiency (Parsimony): The model can characterized the image function with little parameters. • Robustness: Must be stable in the face of perturbation and noise • Computability: Efficient computations of parameters. Signal modeling involves two steps, namely; 1) Model selection: Choosing an appropriate parametric form for the model data 2) Model Parameter determination: Model parameter determination include the determination of model order and model coefficients. Successful application of modeling technique hinges on effi- cient method of model order determination. In this parametric MRI reconstruction, five known modeling technique have been evaluated. These are FPE, AIC, RV, MDL and HNQ. This paper is organized as follows; Section. I gives a brief introduction to MRI reconstruction and its associated terminology. Detail of steps involve in TERA reconstruction is as contained in section II. In Section. III various methods of model order determination would be discussed. Section. V and Section. V-B discusses the result obtained and conclusion respectively. World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:2, No:6, 2008 1834 International Scholarly and Scientific Research & Innovation 2(6) 2008 scholar.waset.org/1307-6892/10711 International Science Index, Computer and Information Engineering Vol:2, No:6, 2008 waset.org/Publication/10711