Real-time tracking of the lesion targets is a critical requirement for precise radiotherapy in the presence of patient breathing. Long scan time is a bottleneck to hamper the application of 4D MRI in LINAC procedures. The aim of this study is to develop techniques for the acceleration of 4D MRI. Pulse sequences using stack-of-stars and 3D ultrashort TE (UTE) were used to acquire highly undersampled data in subjects at free breathing.  Algorithms were developed to explore the sparsity of the data and generate high quality 4D images with an acceleration rate up to 25 in the chest and abdomen. Feasibility of highly accelerated water-fat image is also demonstrated in this study.