In interventional MR, 3D visualization of catheters is hampered by low spatial and temporal resolution as conventional image reconstruction requires data sampling at or above the Nyquist rate. We propose a model-based reconstruction technique to fit a parameterised model of a catheter to acquired MRI data by minimising the -norm in Fourier space. A modelled image of the catheter shape is transformed to the Fourier space and then registered to the acquired data. Thereby the number of independent degrees of freedom to be solved for in reconstruction is reduced. Using computer simulations and phantom data it is demonstrated that the catheter shape can be reconstructed from highly undersampled data indicating the potential of the method for 3D imaging of catheters.