Visual reconstruction
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Convex half-quadratic criteria and interacting auxiliary variables for image restoration
IEEE Transactions on Image Processing
Robust kernel methods for sparse MR image reconstruction
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Fourier synthesis via partially finite convex programming
Mathematical and Computer Modelling: An International Journal
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Combining fast MR acquisition sequences and high resolution imaging is a major issue in dynamic imaging. Reducing the acquisition time can be achieved by using non-Cartesian and sparse acquisitions. The reconstruction of MR images from these measurements is generally carried out using gridding that interpolates the missing data to obtain a dense Cartesian k-space filling. The MR image is then reconstructed using a conventional fast Fourier transform (FFT). The estimation of the missing data unavoidably introduces artifacts in the image that remain difficult to quantify.A general reconstruction method is proposed to take into account these limitations. It can be applied to any sampling trajectory in k-space, Cartesian or not, and specifically takes into account the exact location of the measured data, without making any interpolation of the missing data in k-space. Information about the expected characteristics of the imaged object is introduced to preserve the spatial resolution and improve the signal-to-noise ratio in a regularization framework. The reconstructed image is obtained by minimizing a non-quadratic convex objective function. An original rewriting of this criterion is shown to strongly improve the reconstruction efficiency. Results on simulated data and on a real spiral acquisition are presented and discussed.