CS-Dixon: Compressed Sensing for Water-Fat Dixon Reconstruction

Introduction: Water-fat separation is of interest in several MRI applications including fat suppression and fat quantification. Chemical shift imaging allows robust water-fat separation [1, 2], however the acquisition of multiple images results in prolonged scan time. Accelerated water-fat separation using compressed sensing (CS) was partly addressed in [3] by considering the separation as a spectroscopic problem and exploiting the spectral sparsity in the reconstruction. However, this approach requires data acquisition at multiple echo times (significantly more than 3), prolonging the scan time and limiting the effective acceleration factor. In this work we consider the commonly used three point Dixon approach for water-fat separation. Dixon reconstruction already assumes signal sparsity in the spectral dimension by modeling the signal by a two point spectrum at fixed frequencies. An integrated CS-Dixon algorithm is proposed, which applies a sparsity constraint on the water and fat images and jointly estimates water, fat and field map images. The method allows scan time reduction of above 3 in 3D MRI, fully compensating for the additional time necessary to acquire the chemical shift encoded data. Theory: Compressed sensing [4, 5, 6] is a promising method for scan time reduction by exploiting signal sparsity. Incoherent sampling, signal sparsity and a nonlinear, sparsity promoting reconstruction are the key ingredients of CS. In chemical shift imaging additional subsampling in the chemical shift dimension could be employed resulting in undersampling a higher dimensional kspace, and thus, improved incoherence. Applying a sparsity constraint in the water and fat images effectively exploits that additional subsampling dimension. It can also be assumed that water and fat images are usually sparser than combined images. In chemical shift imaging data are acquired at several different echo times. Denoting the k-space data acquired at echo time with , the measurement vector can be written as , , ... with typically L = 3. The signal model is given by: Δ Δ , where is the Fourier transform, and are the complex water and fat images, Δ is the chemical shift and Δ is the field map. The goal is to find the vector , , from the undersampled measurement data according to the model . The proposed method solves the problem jointly for all voxels, simultaneously updating the water, fat and field map estimates. The CS-Dixon reconstruction problem can be formulated as: argmin | | λ |Ψ | λ |Φ | 1 ,