Citation: Park, S.; Yoo, Y. A New
Fast Logarithm Algorithm Using
Advanced Exponent Bit Extraction
for Software-Based Ultrasound
Imaging Systems. Electronics 2023, 12,
170. https://doi.org/10.3390/
electronics12010170
Academic Editors: Sanjay Misra,
Robertas Damaševiˇcius
and Bharti Suri
Received: 9 November 2022
Revised: 24 December 2022
Accepted: 29 December 2022
Published: 30 December 2022
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Communication
A New Fast Logarithm Algorithm Using Advanced Exponent
Bit Extraction for Software-Based Ultrasound Imaging Systems
Seongjun Park
1,2
and Yangmo Yoo
1,3,
*
1
Department of Electronic Engineering, Sogang University, Seoul 04107, Republic of Korea
2
Department of Computer Science, Sogang University, Seoul 04107, Republic of Korea
3
Department of Biomedical Engineering, Sogang University, Seoul 04107, Republic of Korea
* Correspondence: ymyoo@sogang.ac.kr; Tel.: +82-2-705-8907; Fax: +82-2-707-3008
Abstract:
Ultrasound B-mode imaging provides anatomical images of the body with a high resolution
and frame rate. Recently, to improve its flexibility, most ultrasound signal and image processing
modules in modern ultrasound B-mode imaging systems have been implemented in software. In
a software-based B-mode imaging system, an efficient processing technique for calculating a logarithm
instruction is required to support its high computational burden. In this paper, we present a new
method to efficiently implement a logarithm operation based on exponent bit extraction. In the
proposed method, the exponent bit field is first extracted and then some algebraic operations are
applied to improve its precision. To evaluate the performance of the proposed method, the peak
signal-to-noise ratio (PSNR) and the execution time were measured. The proposed efficient logarithm
operation method substantially reduced the execution time, i.e., eight times, compared to direct
computation while providing a PSNR of over 50 dB. These results indicate that the proposed efficient
logarithm computation method can be used for lowering the computational burden in software-based
ultrasound B-mode ultrasound imaging systems while improving or maintaining the image quality.
Keywords:
ultrasound B-mode imaging; float point logarithm; software-based ultrasound imaging
systems; single instruction multiple data
1. Introduction
A medical ultrasound imaging system can show the anatomical structure of the
body in real time. The reconstruction of ultrasound images has traditionally been imple-
mented using hardware-based signal and image processing engines. Recently, to enhance
their computational flexibility, research on software-based ultrasound imaging systems
has been actively conducted with various advanced computing technologies [
1
–
3
]. For
software-based ultrasound systems, an efficient software implementation method is nec-
essary for supporting the complex signal and image processing blocks demanding high
computational power.
In ultrasound B-mode imaging, log compression has been widely used for empha-
sizing weak scattering signals on the same scale as strong specular reflections [
4
]. In log
compression, the envelope signal, after receive beamforming and quadrature demodula-
tion, is transformed by applying a logarithm operation. Since the computation of logarithm
operations generally requires complex floating operation on software-based ultrasound
imaging systems, it takes a longer execution time. Therefore, to implement a computation-
ally efficient software-based ultrasound imaging system, it is necessary to minimize the
execution time of the logarithm operation.
To lower the computational complexity in logarithm operations, various approxima-
tion methods, such as a look-up table (LUT) and Taylor’s series, have been proposed [
5
,
6
].
In this study, to further lower this computational complexity, a new approximation method,
in which the exponent bits of IEEE 754 floating-point envelope data are utilized, is pre-
sented. The IEEE 754 floating-point format is the standard notation used to represent
Electronics 2023, 12, 170. https://doi.org/10.3390/electronics12010170 https://www.mdpi.com/journal/electronics
