Recent work in k-t BLAST and undersampled projection angiography has emphasized the value of using training data sets obtained during the acquisition of a series of images. These techniques have used iterative algorithms guided by the training set information to reconstruct time frames sampled at well below the Nyquist limit. We present here a simple non-iterative unfiltered backprojection algorithm that incorporates the idea of a composite image consisting of portions or all of the acquired data to constrain the backprojection process. This significantly reduces streak artifacts and increases the overall SNR, permitting decreased numbers of projections to be used when acquiring each image in the image time series. For undersampled 2D projection imaging applications, such as cine phase contrast (PC) angiography, our results suggest that the angular undersampling factor, relative to Nyquist requirements, can be increased from the present factor of 4 to about 100 while increasing SNR per individual time frame. Results are presented for a contrast-enhanced PR HYPR TRICKS acquisition in a volunteer using an angular undersampling factor of 75 and a TRICKS temporal undersampling factor of 3 for an overall undersampling factor of 225. There are many applications for which it is desirable to have high spatial and high temporal resolution. K-space sampling that obeys the Nyquist theorem usually precludes simultaneous achievement of these aims in MR imaging. Among other approaches, radial acquisitions have been proposed for accelerated sampling schemes. Peters (1) and Vigen (2) reported on the use of 3D MR angiography acquisitions in which 2 dimensions were encoded using undersampled projection reconstruction and the third was encoded using phase encoding. In these applications, the projections are rotated around a single axis and, even if the planes containing the projections are completely sampled in the Fourier encoded direction, the undersampling factor, relative to that required by the Nyquist theorem, is limited to about 6 due to the streaks in the axial reformatted images.When radial sampling is extended by distributing the projections in all directions in 3D as in VIPR (3), significantly higher acceleration factors relative to fully sampled acquisition can be achieved. We recently reported on a relatively artifact free PC VIPR (phase contrast Vastly undersampled Isotropic PRojection imaging) acquisition in which an acceleration factor of 61 relative to conventional Cartesian 3D PC was achieved (4). This acceleration factor was defined as the ratio of an imaging speed index for PC VIPR and Cartesian 3D PC acquisitions. This index was determined as the volume covered divided by the product of scan duration times voxel size.Despite such large increases in acquisition speed, some applications would benefit from further accelerations. For example, in recent cine PC VIPR measurements with 3D flow encoding for pressure mapping in 1-2 mm thick vessels using an acquisition matrix of 256 ϫ 256 ϫ 256 voxels and 10 cardiac ph...