Learned Image Representations for Multidimensional Imaging

The recovery of the image data from sub-Nyquist sampled measurements using constrained image models is emerging as a promising approach to accelerate imaging. A challenge in using apriori selected models (eg. Fourier series, sparse wavelet representation) is that such models may not be efficient in representing the signal at hand. Our main focus is to develop novel theoretical framework and efficient algorithms to learn image representations from under-sampled measurements. The representations (blind compressed sensing, blind linear model termed as k-t SLR) enabled several  accelerated MR imaging schemes. The proposed adaptive framework is a significant departure from classical approaches of using pre-determined dictionaries. We have also introduced theoretical guarantees for the recovery of such signals from undersampled data. The proposed framework is demonstrated to outperform classical compressed sensing methods in a range of applications including cardiac CINE MRI, myocardial perfusion MRI, dynamic lung imaging, and multi-parameter mapping where T1rho and T2 is simultaneously measured.