Comparison of Wavelets and a new DCT Algorithm for Sparsely Sampled Reconstruction

1() . minimize m s t F m y Ω Ψ= In equation 1 represents the transform, m the reconstructed image, F the sub sampled Fourier transform matrix and y the k-space samples. For the Wavelet variant of the minimization represents the Wavelet transform, whereas in the DCT variant it represents a windowed version of the DCT. For computing these minimization problems a variant of POCS was implemented. RESULTS In order to compare the DCT and Wavelet based approaches in MRI, two complex images of 256x256 pixels were obtained using a 0.5T Philips Gyroscan scanner. Two knee images were taken in the sagittal and coronal planes using 2DFT spin echo trajectories with TE=30ms and TR=500ms. The DCT approach was compared with Wavelet algorithms using Daubechies 4 and Daubechies 8 Wavelets. All three were implemented with an asymmetric 35% k-space sub sampling using 90 of 256 lines, with 53 central lines. The results were compared with a fully sampled reconstruction using the MSE and PSNR indices given in equations 2 and 3. The reconstructed images are shown in figures 1 and 2 while the performance indices for each method are shown in the table below. 11 2