Abstract: A method of dynamic resonance imaging is provided. A magnetic resonance imaging excitation is applied. Data in 2 or 3 spatial frequency dimensions, and time is acquired, where an acquisition order in at least one spatial frequency dimension and the time dimension are in a pseudo-random order. The pseudo-random order and enforced sparsity constraints are used to reconstruct a time series of dynamic magnetic resonance images.

Abstract: A method of dynamic resonance imaging is provided. A magnetic resonance imaging excitation is applied. Data in 2 or 3 spatial frequency dimensions, and time is acquired, where an acquisition order in at least one spatial frequency dimension and the time dimension are in a pseudo-random order. The pseudo-random order and enforced sparsity constraints are used to reconstruct a time series of dynamic magnetic resonance images.

Abstract: A data processing technique called a Ridgelet transform is disclosed for more efficiently representing information. Original data samples (e.g., in the time domain) are received and transformed into frequency domain values provided in Cartesian coordinates. The frequency domain values provided in Cartesian coordinates are then transformed to digital polar coordinates (provided in a digital polar grid). Because the polar grid is non-uniform, the polar coordinate values can be weighted or normalized. A Wavelet transform is performed on data derived the frequency domain values provided in digital polar coordinates to generate Wavelet coefficients (or Ridgelet coefficients). Next a thresholding or filtering process can be performed on the Ridgelet coefficients to select a group of larger Wavelet coefficients and to discard the remaining Wavelet coefficients.