Ultrasound de-convolution using a Least Angle Regression approach

We address the two main challenges that have so far prevented adaption of chirp transmission in medical ultrasound, despite its potential to achieve a significantly enhanced SNR. The first is the high sidelobe level resulting from signal compression using a matched filter. The second challenge is that the level of the sidelobes is further increased since the pulse is distorted in the body in an unknown manner. This distortion is a result of the frequency dependent absorption in the living tissue. A high sidelobe level is also associated with the fact that due to the variability in the tissue absorption, the pulse shape itself is not known, so that even matched filtering may result in significant errors. In this work we hypothesize that the signal can be modeled as a sum of relatively few `strong reflectors´ that are the main cause of the sidelobes and a large number of relatively `weak´ reflectors. Using this sparsity as a prior, we can solve for the position and (complex) reflectivity of the strong reflectors as well as for the precise form of the pulse shape. This allows the retrieval of the reflectivity function, applying the appropriate matched filter to the signal of `weak´ reflectors. We propose to use a method based on the Least Angle Regression (LARS) algorithm for the solution of the non-linear optimization problem involved in the estimation of the positions and the (generally complex) amplitudes of the strong reflectors, as well as the precise pulse shape anywhere in the tissue.