MRI image reconstruction approach for partial K-space based on the Discrete Fourier Transform in the least square sense

Magnetic Resonance Imaging (MRI) provides important and valuable information (images) about the organs structures and soft tissues non-invasively. In this work, a reconstruction approach using partial k-space, the “Optimized Discrete Fourier Transform” (ODFT), is introduced. The developed approach decomposes the 2-D Fourier Transform (FT) into two steps of 1-D DFT. The corresponding elements along each row or column are estimated using an optimization technique, namely, the complex conjugate gradient. It is proposed to be implemented in conjunction with other techniques to obtain an optimum image that is closer to the original image. The algorithm is evaluated visually and quantitatively using the Performance Test and the Mean Square Error as similarity measures. Also, its effectiveness is compared with different MRI reconstruction techniques such as the Projection onto Convex Set technique, the Conjugate Synthesis technique and the Zero filling technique. The results illustrate that the proposed technique outperforms the conventional MRI image reconstruction techniques.