title: Improvement of penetration of modified amplitude and phase estimation beamformer.
abstract: OBJECTIVE
  High-frame-rate ultrasound is the predominant technique for the measurement of tissue dynamics. It enables an imaging frame rate of over 1 kHz using unfocused transmit beams and parallel receive beamforming. On the other hand, the spatial resolution is degraded compared to the conventional method based on sequential transmissions of focused beams. For improvement of the spatial resolution of high-frame-rate ultrasound, we have investigated a kind of adaptive beamformer, i.e., amplitude and phase estimation (APES) beamformer.
  
  
  METHODS
  In our previous study, it was shown that the APES beamformer realized a significantly better spatial resolution than the conventional delay and sum (DAS) beamformer without sub-array averaging and diagonal loading by considering the directivity of each transducer element. By omitting sub-array averaging and adding sub-aperture beamforming, the computational load could also be reduced significantly. One shortcoming of the proposed APES beamformer with element directivity, i.e., modified APES beamformer, is the degradation of penetration compared with the conventional APES beamformer with sub-array averaging and diagonal loading. In the present study, sub-array averaging and diagonal loading were applied to the modified APES beamformer for the improvement of the penetration.
  
  
  RESULTS
  The conventional and modified APES beamformers realized similar performances when used with sub-array averaging and diagonal loading. Furthermore, the modified APES beamformer realized better spatial resolution and improved penetration when used with sub-aperture beamforming and diagonal loading. The modified APES beamformer with diagonal loading at 0.025 of the received power realized a penetration similar to that of the conventional APES beamformer with sub-array averaging and diagonal loading. The lateral spatial resolutions achieved with the conventional and modified APES beamformers were 0.36 and 0.31 mm, respectively. In addition, the modified APES beamformer could reduce the dimension of the covariance matrix to [Formula: see text], versus [Formula: see text] of the conventional APES beamformer, resulting in a computation time of only 1.1 %.
  
  
  CONCLUSIONS
  Penetration of the modified APES beamformer could be improved significantly by diagonal loading, which hardly increases the computational complexity.
authors.affiliation: Graduate School of Science and Engineering, University of Toyama, Toyama, 930-8555, Japan. hasegawa@eng.u-toyama.ac.jp.
authors.forename: Hideyuki
authors.identifier: http://orcid.org/0000-0003-0709-7821
authors.initials: H
authors.lastname: Hasegawa
mesh_terms: D000465:Algorithms; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D000069453:Ultrasonic Waves; D014463:Ultrasonography / Q000295:instrumentation / Q000379:methods*
keywords: Adaptive beamforming; High-frame-rate ultrasound; Penetration; Spatial resolution