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 narrow band signal, 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 the L1 norm method performs very well even in the presence of moderate noise level for both r.f. and quadrature signals. The time and memory saving in the latter algorithm is remarkable.
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