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:
  1. Select proper wavelet function and the number of decomposition layers. Then do wavelet decomposition to acquired PA signal.
  2. Choose appropriate threshold. Do wavelet coefficient reduction, by either hard thresholding or soft thresholding.
  3. 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.