KEYWORDS
photoacoustic imaging, wavelet
transform, de-noising, in vivo imaging, low-power laser
1 | INTRODUCTION
Photoacoustic imaging (PAI), as a new hybrid imaging modality, combines
the advantages of both optical and ultrasound imaging: the high contrast
of optical imaging and good spatial resolution in deep tissue of
ultrasound imaging1. The PA effect is induced when a
light-absorbing object is exposed to a pulsed light source. When
chromophores (such as melanin, hemoglobin, and water) absorb photons and
undergo nonradiative relaxation, the temperature within the sample rises
sharply, leading to thermoelastic expansion and the emission of
ultrasonic wave. The broadband PA signal is detected by the ultrasound
transducer, followed by signal processing and image reconstruction.
By utilizing the PA effect, PAI technology has been developed fast in
recent decades, including two main categories: PA microscopy (PAM) and
PA tomography (PAT), which targets different application scenarios
requiring different penetration depth or spatial
resolution2. By probing the endogenous chromophores
mentioned above, PAI is able to image from organelles to organs in
vivo3, 4. This new technology has been used in some
preclinical and clinical applications, such as early detection for
breast cancer, skin diseases, and so on5-7.
However, there also exists many challenges in PAI technology for wide
clinical use. One of the challenges is the low SNR of PA
signal8, especially in deep tissue imaging under
limited laser energy. The underlying reason is that energy conversion
efficiency from light to acoustic pressure, arising from the
thermoelastic mechanism, is very low (ranging from
10-12 to 10-8)9.
Additionally, acoustic attenuation and scattering in heterogeneous
biological tissues further contribute to the problem. As a result, the
received PA signal is often weak and strongly distorted, which results
in blurring and artifacts in reconstructed PA image. If the biological
tissue has multiple layers, the problem will be more complex. Due to the
reflection, scattering and attenuation, the upper layer may generate PA
signals with higher intensity and frequency spectrum, e. g. PA signal
from the skin surface, which are usually unwanted signals. On the other
hand, the lower layer may generate PA signals with lower intensity and
frequency spectrum, which exhibits much worse SNR. To alleviate this
problem, there usually exists two main approaches. The first approach is
to increase the laser power, which is ultimately limited by the safety
issue. The other approach is to do multiple signal acquisition and data
averaging, which will severely slow the imaging
speed10.
In practice, signal preprocessing approaches, such as low-pass or
band-pass filtering, is also widely used. It does filter out part of the
noise, but it will also induce PA signal distortion and lose important
details, leading to blurring of PA image. What’s more, it performs even
worse when dealing with multi-layer tissue structure, since different
layer’s PA signals usually shows different frequency characteristics.
Wavelet threshold de-noising (WTD), as a potential signal processing
method, has been applied in de-noising PA signals11.
However, traditional WTD method often exhibit a dilemma: either
excessive de-noising, causing distortion of the PA signals, or weak
de-noising, resulting in inconspicuous noise reduction. Sometimes, it
may go to the other end, inducing more impulse noise. In this paper,
based on the frequency characteristics of the acquired PA signals, we
propose a modified wavelet de-noising method, which can effectively
reduce the noise and maintain the fidelity of PA signal. Both ex vivo
and in vivo experiments were conducted to validate the feasibility of
the proposed method.
2 | WAVELET THRESHOLD DENOISING
2.1 | Principle
Wavelet denoising method is a time-frequency analysis method based on
the wavelet transform (WT) theory. It uses the characteristics of WT
multi-resolution analysis, with less operational complexity.
Suppose the acquired PA signal y(n) of length N is approximately in the
following form:
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ y(n)\ =\ x(n)\ +\ \sigma e(n),\ \ \ 1\leq n\leq\)N
(1)
where x(n) is the clean PA signal, e(n) is the noise, and \(\sigma\) is
the noise’s standard deviation. The purpose of WTD is to recover x(n)
from y(n) with as little distortion as possible12.
In general, noise, mainly in the high frequency, has a larger number of
wavelet coefficients with smaller magnitude, and the target signal,
mainly in the low frequency, has a fewer number of wavelet coefficients
with larger magnitude. According to this property, the basic idea of WTD
is to set the wavelet coefficients below a certain threshold to zero,
and preserve or shrink the wavelet coefficients above the threshold,
corresponding to two coefficients reduction ways: hard thresholding and
soft thresholding, respectively.
The main process of WTD is divided in the following three steps:
- Select proper wavelet function and the number of decomposition layers.
Then do wavelet decomposition to acquired PA signal.
- Choose appropriate threshold. Do wavelet coefficient reduction, by
either hard thresholding or soft thresholding.
- Reconstruct PA signal based on the processed wavelet coefficients, by
inverse wavelet transform13.
There are also some trade-offs to be made during the de-noising process.
The threshold can’t be too large, or it will filter out the useful PA
component. It can’t be too small, either, or it will ignore the noise
with relatively larger energy and adversely affect the de-noising
performance. The same principle is also applicable for the number
selection of decomposition layers. If the number of wavelet
decomposition levels is too high, the useful PA signal may be
compromised. Conversely, if the number of decomposition levels is too
low, it becomes challenging to effectively distinguish between the
signal and the noise.
2.2 | Traditional wavelet threshold selection method
The threshold selection is essential to the wavelet de-noising
performance. There are many traditional threshold selection methods,
such as sqtwolog, rigrsure, heursure, and minimaxi, which will be
introduced below.