Magnetic resonance image reconstruction using the annihilating filter method

Compressed sensing reconstruction algorithms exploit the sparsity of MRI images to significantly undersample the k-space. However, these algorithms are computationally expensive, may be slow to converge, and perform best when the samples are randomly selected. We propose a new sparse reconstruction algorithm based on the annihilating filter method to palliate these issues. This new method is non iterative and does not require random sampling. We demonstrate that our technique outperforms the basis pursuit theoretical limit for very sparse signals. As an application, we show clinical MRI images reconstructed using our method.