High resolution Magnetic Resonance Imaging (MRI) requires long acquisition time to obtain the fully sampled k-space data for image reconstruction. Compressed Sensing (CS) theory has recently been utilized to accelerate the image reconstruction speed by sparsely sampling the k-space. In this work, the CS framework was combined with the Tight Wavelet Frame (TWF) transform to further enhance edges/boundaries of MR images and reduce their noise levels. Because the TWF coefficients at finer scale correspond to important image boundary features, the proposed algorithm is able to effectively enhance the signal to noise ratio of MR images without blurring their edges or create artifacts. The resulting constrained minimization problem is then solved iteratively and requires extensive computational resources. To accelerate the reconstruction for real-time medical image processing purpose, the algorithm is implemented on the General Purpose Graphic Processing Units (GPGPU). The effects of various factors, including the register counts and block size, on the GPU occupancy have been investigated to tune the hardware for the optimum performance. The proposed algorithm demonstrates great potential to accelerate the MR imaging acquisition by 8-fold without noticeable artifacts. Comparisons with other two l1 minimization methods with traditional wavelet transforms further confirm the competitiveness of the proposed algorithm. Moreover, a speedup of 45 times was achieved by the GPGPU implementation compared with the CPU version, and therefore making this algorithm suitable for applications in a clinical MRI setting.