Systems and methods for image reconstruction using variable-density spiral trajectory

A method for image reconstruction, comprising:

• acquiring magnetic resonance data corresponding to an area of interest of a subject, wherein acquiring the magnetic resonance data comprises:
• determining a multi-level undersampling pattern based on:
• a distance between each sampling point of a plurality of sampling points in k-space and a center of the k-space, and
• a probability that each of the sampling points is acquired;
• determining a desired variable-density spiral trajectory based on the multi-level undersampling pattern;
• generating one or more spiral gradient waveforms based on the desired variable-density trajectory;
• tracing a variable-density spiral trajectory using the one or more spiral gradient waveforms;
• and
• sub-sampling the magnetic resonance data based on the variable-density spiral trajectory;
• and
• reconstructing one or more images of the area of interest based on the acquired magnetic resonance data.

A system for image reconstruction, comprising:

• a data collection device configured to acquire magnetic resonance data corresponding to an area of interest of a subject, the data collection device comprising:
• an undersampling determination module configured to determine a 2D multi-level undersampling pattern based on:
• a distance, rk, between each sampling point of a plurality of sampling points in k-space and a center of the k-space, and
• a probability that each of the sampling points is acquired;
• a trajectory determination module configured to determine a desired variable-density spiral trajectory based on the multi-level undersampling pattern, wherein the desired variable-density spiral trajectory has a density according to a function of rk;
• a generating module configured to generate one or more spiral gradient waveforms based on the desired variable-density trajectory;
• a tracing module configured to trace a variable-density spiral trajectory using the one or more spiral gradient waveforms;
• and
• a sampling module configured to sub-sample the magnetic resonance data based on the variable-density spiral trajectory;
• and
• an image processing device coupled to the data collection device and configured to reconstruct, using one or more image reconstruction functions that comprise compressed sensing, one or more images of the area of interest based on the acquired magnetic resonance data.

A non-transitory computer-readable storage medium having stored computer-executable instructions that, when executed by one or more processors, cause a computer to perform functions comprising:

• acquiring magnetic resonance data corresponding to an area of interest of a subject, wherein acquiring the magnetic resonance data comprises:
• determining a multi-level undersampling pattern based on:
• a distance between each sampling point of a plurality of sampling points in k-space and a center of the k-space, and
• a probability that each of the sampling points is acquired;
• determining a desired variable-density spiral trajectory based on the multi-level undersampling pattern;
• generating one or more spiral gradient waveforms based on the desired variable-density trajectory;
• tracing a variable-density spiral trajectory using the one or more spiral gradient waveforms;
• and
• sub-sampling the magnetic resonance data based on the variable-density spiral trajectory;
• and
• reconstructing one or more images of the area of interest based on the acquired magnetic resonance data.