Incorporating self-referenced information into Compressed Sensing in dynamic imaging

Introduction: Compressed sensing (CS) is a newly developed fast imaging technique aimed at robustly recovering image data from partially-sampled k-space data.[1, 2] The Orthogonal Matching Pursuit (OMP) was suggested for solving medium-sized CS problems [3]. As OMP requires precisely sparse data to operate on, previous work employed a combination of constrained random sampling in k-t space along with a penalty function to improve reconstruction, in the context of dynamic MR imaging. In previous work, the penalty function was obtained by performing a first pass through the reconstruction algorithm, by estimating the density of non-zero pixels in the reconstructed result. Subsequently, this density map gets used into a second and final pass through the reconstruction algorithm, along with the original undersampled data (OMP + Density Penalty). While this approach is sound, long processing time is a main limitation of the CS approach and having to perform the reconstruction twice compounds the problem. In order to shorten computation time, an alternative scheme is proposed here that involves using the fully sampled central k-space data to generate a ‘self-referenced’ penalty function (self-referenced OMP). As a result, there is no need for an extra OMP processing to estimate the penalty function, as it has been obtained instead at the acquisition stage. Furthermore, as demanded by CS, this sampling scheme also satisfies the Uniform Uncertainty Principle for compressive sampling, a fundamental requirement of CS, hence the central fully sampled data can also be incorporated into the reconstruction. As a further benefit of our proposed approach, the more densely sampled central region can also help reduce signal interference and improve reconstruction. The need to increase density near k-space center while keeping the acceleration unchanged does however lead to a small decrease in density in outer k-space regions, which might translate into spatial blurring.