A Robust Compressive Sampling Method for MR Images Based on Partial Scanning and Apodization

This paper proposes a robust, fast Magnetic Resonance Imaging (MRI) reconstruction algorithm. The method is based on Compressive Sampling (CS), profile of the k-space coefficients and sparsity in the wavelet transform domain. It commences with partial acquisition of the k-space of the image followed by random sampling prior to reconstruction in the wavelet transform domain using a greedy algorithm. The reconstructed wavelet coefficients vector is transformed into the full k-space vector of the image by determining its Inverse Discrete Wavelet Transform (IDWT) domain. The vectorized form of the k-space reveals the reconstruction artifacts which makes it easy to design a denoising filter. The artifacts are then suppressed using an apodization function. The denoised coefficients are then reshaped into a k-space matrix prior to being transformed into the reconstructed image using two-dimensional Inverse Discrete Fourier Transform (2D-IDFT). The Structural SIMilarity (SSIM) and the Peak Signal to Noise Ratio (PSNR) quality metrics are used for quality assessment of the output images. Experimental results show that the proposed method yields an average PSNR improvement of 1.4 dB over the Orthogonal Matching Pursuit (OMP) method at 40% measurements. The improvement implies reduction in scan time by approximately 10% for a given image quality.