Nonlinear pth root spectral magnitude scaling beamforming for clinical photoacoustic and ultrasound imaging
Seonghee Cho, Seungwan Jeon, Wonseok Choi, Ravi Managuli, Chulhong Kim
Abstract
A recently introduced nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> </mml:math> th root delay-and-sum ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>NL-</mml:mtext> </mml:mrow> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>-DAS</mml:mtext> </mml:mrow> </mml:math> ) beamforming (BF) technique for ultrasound (US) and photoacoustic (PA) imaging, achieving better spatial and contrast resolution compared to a conventional delay and sum (DAS) technique. While the method is advantageous for better resolution, it suffers from grainy speckles and dark areas in the image mainly due to the interference of non-sinusoidal functions. In this Letter, we introduce a modified <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>NL-</mml:mtext> </mml:mrow> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>-DAS</mml:mtext> </mml:mrow> </mml:math> technique called nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> </mml:math> th root spectral magnitude scaling ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>NL-</mml:mtext> </mml:mrow> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>-SMS</mml:mtext> </mml:mrow> </mml:math> ), which performs the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> </mml:math> th root on the spectral magnitude instead of the temporal amplitude. We evaluated the US and PA images of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>NL-</mml:mtext> </mml:mrow> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>-SMS</mml:mtext> </mml:mrow> </mml:math> against those of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>NL-</mml:mtext> </mml:mrow> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>-DAS</mml:mtext> </mml:mrow> </mml:math> by comparing the axial and lateral line profiles, contrasts, and contrast-to-noise ratios (CNRs) in both phantom and in vivo imaging studies with various <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> </mml:math> values. As a result, we found that the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>NL-</mml:mtext> </mml:mrow> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>-SMS</mml:mtext> </mml:mrow> </mml:math> has better axial resolution and CNR than the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>NL-</mml:mtext> </mml:mrow> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>-DAS</mml:mtext> </mml:mrow> </mml:math> , and reduces the grainy speckles and dark area artifacts. We believe that, with this enhanced performance, our proposed approach could be an advancement compared to the existing nonlinear BF algorithms.