IEEE SIGNAL PROCESSING LETTERS, VOL. 22, NO. 12, DECEMBER 2015 2479
Noncontact Vital Sign Detection based on
Stepwise Atomic Norm Minimization
Li Sun, Hong Hong, Member, IEEE, Yusheng Li, Chen Gu, Feng Xi, Member, IEEE,
Changzhi Li, Senior Member, IEEE, and Xiaohua Zhu, Member, IEEE
Abstract—Noncontact techniques for detecting vital signs have
attracted great interest due to the benefits shown in medical mon-
itoring and military applications. A rapid remote evaluation on
physiological signal frequencies is needed in search and rescue op-
erations as well as intensive care. However, the presence of respira-
tion harmonics causes aliasing problems to heart-rate estimation,
especially when the data volume is limited. By taking advantage
of the simple pattern of physiological signals, we propose a step-
wise atomic norm minimization method (StANM) to accurately as-
sess the respiration and heartbeat frequencies with a limited data
volume. First, the respiration frequency is estimated by the conven-
tional atomic norm minimization. Then the frequencies of respira-
tion harmonics are generated based on the inherent relationship
between the fundamental tone and the harmonics. Finally, with
the pre-estimated frequencies, we locate the heartbeat frequency
by solving a modified atomic norm minimization problem. Simu-
lations and experiments show that the proposed method can accu-
rately estimate physiological frequencies from 6.5-second-long raw
data with a 4-Hz sampling rate.
Index Terms—Atomic norm minimization, line spectral estima-
tion, noncontact, super-resolution, vital sign detection.
I. INTRODUCTION
I
N RECENT years, noncontact vital sign detection tech-
nology has attracted great interest in various fields, such
as medical monitoring,
military applications, security and
counter-terrorism action as well as search and rescue operations
[1], [2]. It not only significantly extends the time that human
subjects can be monit
ored, but also enables investigations on
special problems such as empyrosis, and avoids the negative
impact to measurement accuracy due to psychological factors.
In some special me
dical applications such as intensive care,
postoperative recovery of patients and monitoring of patients
Manuscript received July 01, 2015; revised September 25, 2015; accepted
October 21, 2015. Date of publication October 26, 2015; date of current ver-
sion October 30, 2015. This work was supported by the Special Foundation
of China Postdoctoral Science under Grant 2013T6054, the National Natural
Science Foundation of China under Grant 61301022, the Clinical Special Sci-
ence Foundation of Science and Technology Department of Jiangsu Province
under Grant BL2012062, and by the the Natural Science Foundation of Jiangsu
Province under Grant SBK2014043201. The associate editor coordinating the
review of this manuscript and approving it for publication was Prof. Mehdi
Moradi.
L. Sun, H. Hong, Y. Li, C. Gu, F. Xi, and X. Zhu are with the School of Elec-
tronic and Optical Engineering, Nanjing University of Science and Technology,
Nanjing 210094, China (e-mail: isunly@gmail.com; hongnju@njust.edu.cn).
C. Li is with the Department of Electrical and Computer Engineering, Texas
Tech University, Lubbock, TX 79409 USA (e-mail: changzhi.li@ttu.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LSP.2015.2494604
with severe trauma, a quick assessment of vital signs is of
great importance for doctors to provide care. Also, prompt
noncontact vital sign detection is crucial for quick evaluation
of the status of soldiers on battlefield and search and rescue of
trapped victims after earthquakes and fire disasters.
Existing baseband signal processing algorithms for noncon-
tact vital sign detection are mainly based on the discrete Fourier
transform (DFT). However, due to the smearing and leakage
problems caused by limited data volume, the use of DFT suf-
fers from significant performance degradation. In the previous
attempts to improve the performance, Li et al. triedtoadopta
parametric and cyclic optimization algorithm, namely, RELAX
[3]. Simulation results showed that, for a 12.015-second-long
data sampled at 20 Hz, this algorithm can separate the heartbeat
component from the third-orderharmonicofrespirationwith
a frequency separation of 3 bpm. In 2013, the multiple signal
classification (MUSIC) algorithm was applied to this field [4].
Experiments have demonstrated its feasibility in accurately es-
timating the heartbeat frequency during 8-28 s time intervals
with a sampling rate of 100 Hz. Although via the RELAX and
the MUSIC, the smearing and leakage problems can be allevi-
ated to some extent, the required data volume is still quite large,
which restricts their applications in short-time processing.
In an attempt to accurately assess respiration and heartbeat
frequencies with a limited data length and a low sampling
rate, we propose a novel method based on a stepwise version
of the recently proposed atomic norm minimization (ANM)
approach, which is proved to have a super-resolution capability
with time-limited measurements [5]–[9]. In the next section,
we will describe in detail how the aliasing problems are caused
and what the harmful effects are. Then, the proposed method,
namely, stepwise atomic norm minimization (StANM) will
be elaborated in Section III, after a brief introduction on con-
ventional ANM. Simulations and experiments are presented
in Section IV to show the super-resolution capability of the
StANM with a limited data volume. A conclusion will be
provided in Section V.
II. P
ROBLEM DESCRIPTION
Noncontact CW Doppler radars detect vital signs based on
phase estimation of the signal reflected by a target [1]. The phase
shift is generated by the time-varying displacement
of the
target, which can be expressed as
(1)
where
and represent the heartbeat and respiration
movements which can be approximated as sinusoidals with am-
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