Compressive sensing MRI using dual tree complex wavelet transform with wavelet tree sparsity

Magnetic resonance imaging is one of the most accurate imaging techniques that can be used to detect several diseases, where other imaging methodologies fail. Long scanning time is one of most serious drawback of the MRI modality. Compressed sensing contributed in solving this drawback and decrease the acquisition time of MRI images by reducing the quantity of the measured data that are desirable for reconstruction of an image. In this paper, a new scheme has been realized to reconstruct a high-quality image from smaller amount of measured data. The realized algorithm opportunists the sparsity of the finite difference and the wavelet tree sparsity side by side with the dual-tree wavelet transform as sparsifying transform, by manipulating them in the reconstruction problem as regularization terms. Indeed, exploiting the sparsity of wavelet tree achieves further lessening in the amount of measured data that are needed for the reconstruction, while the utilization of the dual tree wavelet transform as sparsifying transform mitigates the shortcomings of the usage of conventional wavelet transforms in the reconstruction problem. Our technique boosts the signal-to-noise ratio of the image to be reconstructed against the state-of-the-art methods.