Reconstruction Algorithm For Photoacoustic Imaging Research Articles

Tutorial on Development of 3D Vasculature Digital Phantoms for Evaluation of Photoacoustic Image Reconstruction Algorithms

A synthetic phantom model is typically utilized to evaluate the initial performance of a photoacoustic image reconstruction algorithm. The characteristics of the phantom model (structural, optical, and acoustic) are required to be very similar to those of the biological tissue. Typically, generic two-dimensional shapes are used as imaging targets to calibrate reconstruction algorithms. However, these structures are not representative of complex biological tissue, and therefore the artifacts that exist in reconstructed images of biological tissue vasculature are ignored. Real data from 3D MRI/CT volumes can be extrapolated to create high-quality phantom models; however, these sometimes involve complicated pre-processing and mostly are challenging, due to the inaccessibility of these datasets or the requirement for approval to utilize the data. Therefore, it is necessary to develop a 3D tissue-mimicking phantom model consisting of different compartments with characteristics that can be easily modified. In this tutorial, we present an optimized development process of a generic 3D complex digital vasculature phantom model in Blender. The proposed workflow is such that an accurate and easily editable digital phantom can be developed. Other workflows for creating the same phantom will take much longer to set up and require more time to edit. We have made a few examples of editable 3D phantom models, which are publicly available to test and modify.

End-to-end Res-Unet based reconstruction algorithm for photoacoustic imaging.

Recently, deep neural networks have attracted great attention in photoacoustic imaging (PAI). In PAI, reconstructing the initial pressure distribution from acquired photoacoustic (PA) signals is a typically inverse problem. In this paper, an end-to-end Unet with residual blocks (Res-Unet) is designed and trained to solve the inverse problem in PAI. The performance of the proposed algorithm is explored and analyzed by comparing a recent model-resolution-based regularization algorithm (MRR) with numerical and physical phantom experiments. The improvement obtained in the reconstructed images was more than 95% in pearson correlation and 39% in peak signal-to-noise ratio in comparison to the MRR. The Res-Unet also achieved superior performance over the state-of-the-art Unet++ architecture by more than 18% in PSNR in simulation experiments.

Solvability for Photoacoustic Imaging With Idealized Piezoelectric Sensors.

Most reconstruction algorithms for photoacoustic imaging assume that the pressure field is measured by the ultrasound sensors placed on a detection surface. However, such sensors do not measure pressure exactly due to their nonuniform directional and frequency responses, and resolution limitations. This is the case for piezoelectric sensors that are commonly employed for photoacoustic imaging. In this article, using the method of matched asymptotic expansions and the basic constitutive relations for piezoelectricity, we propose a simple mathematical model for piezoelectric transducers. The approach simultaneously models how the pressure waves induce the piezoelectric measurements and how the presence of the sensors affects the pressure waves. Using this model, we analyze whether the data gathered by the piezoelectric sensors lead to the mathematical solvability of the photoacoustic imaging problem. We conclude that this imaging problem is well posed in certain normed spaces and under a geometric assumption. We also propose an iterative reconstruction algorithm that incorporates the model for piezoelectric measurements. A numerical implementation of the reconstruction algorithm is presented.

Vector extrapolation methods for accelerating iterative reconstruction methods in limited-data photoacoustic tomography.

As limited data photoacoustic tomographic image reconstruction problem is known to be ill-posed, the iterative reconstruction methods were proven to be effective in terms of providing good quality initial pressure distribution. Often, these iterative methods require a large number of iterations to converge to a solution, in turn making the image reconstruction procedure computationally inefficient. In this work, two variants of vector polynomial extrapolation techniques were deployed to accelerate two standard iterative photoacoustic image reconstruction algorithms, including regularized steepest descent and total variation regularization methods. It is shown using numerical and experimental phantom cases that these extrapolation methods that are proposed in this work can provide significant acceleration (as high as 4.7 times) along with added advantage of improving reconstructed image quality.

Implementation of 2-Dimensional Medical Image Reconstruction Algorithm for Photoacoustic Imaging

In this paper, we review and discuss our proposed image reconstruction algorithm for two dimensional stereo photo-acoustic medical imaging system. The proposed algorithms aim to evaluate the existence possibility of acoustic source within a search area by using the geometric information which is the distance between each sensor element of ultrasound probe and corresponding searching point. Besides, we implemented the hardware and software aspects of an photo-acoustic imaging system that is described in hardware implementation section of this paper. At the end of this paper, some simulation results are presented which utilized the proposed algorithm while compared the image quality of its and conventional k-wave algorithm in which FFT should be used. The simulation results proved the effectiveness of the proposed reconstruction algorithm.

Quantitative photoacoustic image reconstruction improves accuracy in deep tissue structures.

Photoacoustic imaging (PAI) is emerging as a potentially powerful imaging tool with multiple applications. Image reconstruction for PAI has been relatively limited because of limited or no modeling of light delivery to deep tissues. This work demonstrates a numerical approach to quantitative photoacoustic image reconstruction that minimizes depth and spectrally derived artifacts. We present the first time-domain quantitative photoacoustic image reconstruction algorithm that models optical sources through acoustic data to create quantitative images of absorption coefficients. We demonstrate quantitative accuracy of less than 5% error in large 3 cm diameter 2D geometries with multiple targets and within 22% error in the largest size quantitative photoacoustic studies to date (6cm diameter). We extend the algorithm to spectral data, reconstructing 6 varying chromophores to within 17% of the true values. This quantitiative PA tomography method was able to improve considerably on filtered-back projection from the standpoint of image quality, absolute, and relative quantification in all our simulation geometries. We characterize the effects of time step size, initial guess, and source configuration on final accuracy. This work could help to generate accurate quantitative images from both endogenous absorbers and exogenous photoacoustic dyes in both preclinical and clinical work, thereby increasing the information content obtained especially from deep-tissue photoacoustic imaging studies.

Comparison of photoacoustic image reconstruction algorithms using the channelized Hotelling observer

We demonstrate the use of task-based image-quality metrics to compare various photoacoustic image-reconstruction algorithms, including a method based on the pseudoinverse of the system matrix, simple backprojection, filtered backprojection, and a method based on the Fourier transform. We use a three-dimensional forward model with a linear transducer array to simulate a photoacoustic imaging system. The reconstructed images correspond with two-dimensional slices of the object and are 128×128 pixels. In order to compare the algorithms, we use channelized Hotelling observers that predict the detection ability of human observers. We use two sets of channels: constant Q and difference of Gaussian spatial frequency channels. We look at three tasks, identification of a point source in a uniform background, identification of a 0.5-mm cube in a uniform background, and identification of a point source in a lumpy background. For the lumpy background task, which is the most realistic of the tasks, the method based on the pseudoinverse performs best according to both sets of channels.

Compensation of Finite Bandwidth Effect by Using an Optimal Filter in Photoacoustic Imaging

Most existing reconstruction algorithms for photoacoustic imaging (PAI) assume that transducers used to receive ultrasound signals have infinite bandwidth. When transducers with finite bandwidth are used, this assumption may result in reduction of the imaging contrast and distortions of reconstructed images. In this paper, we propose a novel method to compensate the finite bandwidth effect in PAI by using an optimal filter in the Fourier domain. Simulation results demonstrate that the use of this method can improve the contrast of the reconstructed images with finite-bandwidth ultrasound transducers.

Frequency-radial duality based photoacoustic image reconstruction

Photoacoustic image reconstruction algorithms are usually slow due to the large sizes of data that are processed. This paper proposes a method for exact photoacoustic reconstruction for the spherical geometry in the limiting case of a continuous aperture and infinite measurement bandwidth that is faster than existing methods namely (1) backprojection method and (2) the Norton-Linzer method [S. J. Norton and M. Linzer, "Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solution for plane, cylindrical and spherical apertures," Biomedical Engineering, IEEE Trans. BME 28, 202-220 (1981)]. The initial pressure distribution is expanded using a spherical Fourier Bessel series. The proposed method estimates the Fourier Bessel coefficients and subsequently recovers the pressure distribution. A concept of frequency-radial duality is introduced that separates the information from the different radial basis functions by using frequencies corresponding to the Bessel zeros. This approach provides a means to analyze the information obtained given a measurement bandwidth. Using order analysis and numerical experiments, the proposed method is shown to be faster than both the backprojection and the Norton-Linzer methods. Further, the reconstructed images using the proposed methodology were of similar quality to the Norton-Linzer method and were better than the approximate backprojection method.

On the use of frequency-domain reconstruction algorithms for photoacoustic imaging

We investigate the use of a frequency-domain reconstruction algorithm based on the nonuniform fast Fourier transform (NUFFT) for photoacoustic imaging (PAI). Standard algorithms based on the fast Fourier transform (FFT) are computationally efficient, but compromise the image quality by artifacts. In our previous work we have developed an algorithm for PAI based on the NUFFT which is computationally efficient and can reconstruct images with the quality known from temporal backprojection algorithms. In this paper we review imaging qualities, such as resolution, signal-to-noise ratio, and the effects of artifacts in real-world situations. Reconstruction examples show that artifacts are reduced significantly. In particular, image details with a larger distance from the detectors can be resolved more accurately than with standard FFT algorithms.

A Reconstruction Algorithm for Photoacoustic Imaging Based on the Nonuniform FFT

Fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates artifacts in reconstructed images. We propose a novel reconstruction algorithm that applies the one-dimensional nonuniform fast Fourier transform to photoacoustic imaging. It is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of Fourier reconstruction.

Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom studies in a spherical scanning geometry

In this paper, we present a series of phantom experiments that aim to systematically evaluate the possibility of quantitative three-dimensional (3D) photoacoustic imaging of the finger joints in a spherical scanning geometry. The 3D absorption coefficient images of the joint-mimicking phantoms are obtained using our finite-element-based photoacoustic image reconstruction algorithm coupled with the photon diffusion equation. The results show that a 1 mm thick ‘cartilage’ can be accurately differentiated from the ‘bones’ with a 1 MHz transducer. In addition, the absorption coefficient of the ‘cartilage’ can be effectively recovered when this optical property is varied from 0.015 to 0.04 mm−1. The phantom images shown in this paper suggest that 3D photoacoustic tomography in a spherical scanning geometry has the potential to image a realistic human joint.

Quantitative three-dimensional photoacoustic tomography of the finger joints: an in vivo study.

We present for the first time in vivo full three-dimensional (3-D) photoacoustic tomography (PAT) of the distal interphalangeal joint in a human subject. Both absorbed energy density and absorption coefficient images of the joint are quantitatively obtained using our finite-element-based photoacoustic image reconstruction algorithm coupled with the photon diffusion equation. The results show that major anatomical features in the joint along with the side arteries can be imaged with a 1-MHz transducer in a spherical scanning geometry. In addition, the cartilages associated with the joint can be quantitatively differentiated from the phalanx. This in vivo study suggests that the 3-D PAT method described has the potential to be used for early diagnosis of joint diseases such as osteoarthritis and rheumatoid arthritis.

Photoacoustic imaging with a planar measurement array: Improving the resolution using image sources

Biomedical photoacoustic (PA) imaging is a soft‐tissue imaging modality that combines the high spatial resolution of ultrasound (US) with the contrast and spectroscopic opportunities afforded by imaging optical absorption. Exact reconstruction algorithms for PA imaging have been described for spherical, cylindrical, and planar sensor arrays. Many applications to date have used a cylindrical measurement geometry because a single US transducer may be scanned straightforwardly in a circle around a sample. However, planar US arrays composed of piezo or optical elements with small element sizes and fast acquisition times are readily available, making them an attractive option for imaging applications. To capture sufficient data for an exact PA reconstruction with a planar geometry requires an infinitely wide array. In practice, of course, it will be finite, resulting in a loss of resolution and introducing artefacts into the image. To overcome this limitation, it is proposed that acoustic image sources are used to generate a periodically repeating sound field that can be reconstructed exactly from measurements made over a finite aperture. [This work was funded by the EPSRC, UK]

Finite-element-based photoacoustic tomography: phantom and chicken bone experiments

We describe a photoacoustic image reconstruction algorithm that is based on the finite-element solution to the photoacoustic wave equation in the frequency domain. Our reconstruction approach is an iterative Newton method coupled with combined Marquardt and Tikhonov regularizations that can extract the spatial distribution of optical-absorption property in heterogeneous media. We demonstrate this algorithm by using phantom and chicken bone measurements from a circular scanning photoacoustic tomography system. The results obtained show that millimeter-sized phantom objects and chicken bones and/or joints can be clearly detected using our finite-element-based photoacoustic tomography method.