Compressed sensing with a jackknife and a bootstrap

Abstract

Compressed sensing proposes to reconstruct more degrees of freedom in a signal than the number of values actually measured. Compressed sensing therefore risks introducing errors -inserting spurious artifacts or masking the abnormalities that medical imaging seeks to discover. The present case study of estimating errors using the standard statistical tools of a jackknife and a bootstrap yields error "bars" in the form of full images that are remarkably representative of the actual errors (at least when evaluated and validated on data sets for which the ground truth and hence the actual error is available). These images show the structure of possible errors -without recourse to measuring the entire ground truth directly -and build confidence in regions of the images where the estimated errors are small.

Suremap: Predicting Uncertainty in Cnn-Based Image Reconstructions Using Stein’s Unbiased Risk Estimate

“…Alternatively, when dealing with probabilistic neural networks, as exemplified by variational autoencoders [15], one can sample from p(x|y), and thereby reason about the variance, but not the bias, associated with the reconstruction x [16]. Similarly, bootstrap and jacknife resampling methods [17] as well as a combination of variational dropout and input-dependent noise models [18] can be used to estimate the variance of a reconstruction. One can even train a CNN to identify motion artifacts [19].…”

Reducing Uncertainty in Undersampled MRI Reconstruction With Active Acquisition

“…Compressed Sensing (CS)) as well as machine learning ones. On one hand, CS-based MRI reconstruction has been widely studied in the literature [26,28,25,31,40]. These approaches usually result in over-smoothed reconstructions, which involve a time consuming optimization process, limiting their practical scalability.…”