Three dimensional (3D) Magnetic Resonance Imaging (MRI) reconstructions depend heavily on the imaging speed. Magnetic Resonance (MR) images consist of large volume of redundant and sparse data. Therefore, the need to reduce this data without degrading the image information. In Fourier Domain, sparse nature of MR images enables image reconstruction with fewer Fourier coefficients. Fourier Transform (FT) maps the image into the frequency domain using fixed and same size window throughout the analysis. In our paper, a method to perform compressive sensing for MR image is presented. Anisotropic filtering using Active Contour Modelling is performed to smoothen the image in order to preserve edge information. MR image is converted into Fourier Domain using Discrete Fourier Transform (DFT). l1 and l2 reconstruction algorithms are used to reconstruct the images using minimum coefficients that have maximum information.