A practical application of L1 deconvolution for medical ultrasound

The L1 norm (absolute error minimization) deconvolution was applied to medical ultrasound. Its implementation requires a large amount of memory and computing time. A quadrature form of L1 norm deconvolution was derived for narrowband signals, which not only greatly reduced the size of the problem but also lessened the effects of undersampling on medium reflectivities. Preliminary tests on simulated and experimental data showed that L1 norm method performs very well even in the presence of a moderate noise level for both RF and quadrature signals. The time and memory saving in the latter algorithm is remarkable