Random Incident Sound Waves for Fast Compressed Pulse-Echo Ultrasound Imaging

Martin just sent me the following

Dear Igor, 

I recently discovered your post about the paper "Compressive 3D ultrasound imaging using a single sensor" (http://advances.sciencemag.org/content/3/12/e1701423) by Kruizinga et al. (https://nuit-blanche.blogspot.de/2017/12/compressive-3d-ultrasound-imaging-using.html) and read it with great interest. Thank you very much for highlighting this important contribution! I have been working on the incorporation of CS into ultrasound imaging for several years now (https://scholar.google.de/citations?user=X35rUbAAAAAJ&hl=de) and independently discovered a very similar method for high-frame rate ultrasound imaging (UI). Instead of minimizing the number of sensors, this method aims at minimizing the number of sequential pulse-echo measurements per image. It emits three types of random ultrasonic waves to reduce the coherence of the sound waves scattered by distinct basis functions, e.g. point-like scatterers or Fourier basis functions. The synthesis of these waves exploits the degrees of freedom provided by modern UI systems combined with planar transducer arrays. Specifically, it leverages random time delays, random apodization weights, and combinations thereof. (In essence, the method electronically realizes the fixed coding mask used by Kruizinga et al. as one type of random incident ultrasonic wave.) arXiv.org provides a preprint of this work: https://arxiv.org/abs/1801.00205

I hope that my method appeals to you and the readers of your blog. It would also mean a lot to me, if you mentioned this work on occasion.

Happy new year and keep up your good work

Thank you Martin ! Here is the paper:

Random Incident Sound Waves for Fast Compressed Pulse-Echo Ultrasound Imaging by Martin F. Schiffner

A novel method for the fast acquisition and the recovery of ultrasound images disrupts the tradeoff between the image acquisition rate and the image quality. It recovers the spatial compressibility fluctuations in weakly-scattering soft tissue structures from only a few sequential pulse-echo measurements of the scattered sound field. The underlying linear inverse scattering problem uses a realistic d-dimensional physical model for the pulse-echo measurement process, accounting for diffraction, the combined effects of power-law absorption and dispersion, and the specifications of a planar transducer array. Postulating the existence of a nearly-sparse representation of the spatial compressibility fluctuations in a suitable orthonormal basis, the compressed sensing framework ensures its stable recovery by a sparsity-promoting ℓq-minimization method, if the pulse-echo measurements of the individual basis functions are sufficiently incoherent. The novel method meets this condition by leveraging the degrees of freedom in the syntheses of the incident ultrasonic waves. It emits three types of random ultrasonic waves that outperform the widely-used steered quasi-plane waves (QPWs). Their synthesis applies random time delays, apodization weights, or combinations thereof to the voltage signals exciting the individual elements of the planar transducer array.

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