In this project, we are developing a technique for fast and accurate reconstruction of MRI images from undersampled k-space data. Using the fact that MRI images are sparse in wavelet basis, the reconstruction process is framed as an optimization problem in which the cost function consists of two terms: a data fidelity term and a sparsity promoting regularization term. For the sparsity enhancing term, we are using a smooth approximation of the L^p norm (p<1) of the wavelet coefficients of the image. Exploiting the efficient filterbank implementations of wavelet analysis and synthesis transforms , we are developing a preconditioned gradient search where the preconditioner is obtained from an approximation of the Hessian of the cost function. This preconditioner will be implemented without explicitly constructing any matrices.