Photoacoustic imaging is an innovative imaging technique to image biomedical tissues. The time reversal reconstruction algorithm in which a numerical model of the acoustic forward problem is run backwards in time is widely used. In the paper, a time reversal reconstruction algorithm based on particle swarm optimization (PSO) optimized support vector machine (SVM) interpolation method is proposed for photoacoustics imaging. Numerical results show that the reconstructed images of the proposed algorithm are more accurate than those of the nearest neighbor interpolation, linear interpolation, and cubic convolution interpolation based time reversal algorithm, which can provide higher imaging quality by using significantly fewer measurement positions or scanning times.

Recently, photoacoustic tomography (PAT) has emerged as a powerful imaging technology for many biomedical applications [

In a word, the image reconstruction progress can be regarded as running a numerical model of forward problem backwards in time domain, at each time step, in which the measured time-varying pressure signals are enforced (in time reversed order) as a Dirichlet boundary condition at their recorded positions that is called time reversal reconstruction method. It has been described as the “least restrictive” imaging algorithm on the basis that it relies on fewer assumptions than many other imaging reconstruction algorithms [

In conventional time reversal imaging reconstruction, the recorded pressure time series are enforced in time reversed order as a Dirichlet boundary condition as the position of detectors on the measurement surface. If a sparse array of the detectors points is used to collect the measurement rather than a continuous surface, the enforced time reversed boundary condition will necessarily be discontinuous. This can cause significant blurring in the reconstructed images. To solve the problem, Treeby and Cox [

In this paper, what we are concerned with in the method is the artifacts elimination and interaction of image reconstruction when using “time reversal” algorithm. An optimized hybrid interpolation algorithm has been used to create a continuous surface that is spatially equivalent to the original Cartesian measurement surface via interpolation. It is demonstrated that the proposed algorithm can reduce artifact and improve the acoustic magnitude and the signal-to-noise ratio through partial correction for the discontinuous aperture.

For PAT, in a lossless acoustic medium, the photoacoustic wave equation can be reformulated as an initial value problem. The photoacoustic forward problem may be written as

In PAT, the photoacoustic image reconstruction problem is to estimate the initial pressure distribution

During the time reversal reconstruction, if

The essence of the support vector machine (SVM) training parameter selection is a process of optimization search [

The particle swarm optimization (PSO) algorithm is a kind of bionic optimization algorithm, which is derived from the approximation behavior simulation of birds and fish population. It is an optimization tool based on iteration, searching for the optimal solution through the collaboration of the individual particles. The algorithm has a strong ability in global optimization. Using the particle swarm optimization algorithm to solve the optimization problem is equal to the search for the space location of a bird. The birds in the space are called “particles.” Each particle adjusts its flight path randomly based on the flight experience of its own so as to close to the optimal point finally. Different particle has different location and speed and individual fitness corresponding to the flight objective function. The flight path is adjusted by tracking two “extreme values.” One of the extreme values is called individual extremum which indicates the optimal solution of the particle itself. The other one is the global extremum, which indicates the optimal solution of the whole swarm. When the two extreme values are found, the particles update their speed and locations as follows:

Using the particle swarm optimization algorithm to solve the optimization problem is mainly discussing the optimization problem of the penalty factor

The process of specification of PSO-SVM method.

In the process of the SVM interpolation, the solution data in solution space cannot be solved by PSO algorithm directly. The right way is to encode it and convert to particle string structure of the searching space to solve the optimization problem. In the process of the optimization, there are three optimization parameters to be solved, which mean that the dimension of the particle location is three, as

The initial pressure distribution of a phantom (simulating tumor tissue) with a 256 × 256 pixel grid is shown in Figure

PAT image of phantom: (a) initial pressure distribution; (b) conventional time reversal reconstruction.

Pressure distribution of initial pressure and conventional time reversal reconstruction.

The algorithm above is slow for real-time applications. Recently fast PSO optimized SVM interpolation algorithm has been developed [

The simulation is performed on grid architecture with 5% and 15% Gaussian White Noise (GWN) added to the recorded photoacoustic data, respectively. The PC with Intel P6300 CPU and 4 GB RAM is used in the simulation. The propagation velocity of sound in the medium is 1500 m/s, the medium density is 1000 kg/m^{3}, and the initial pressure distribution is the two locations in the spherical absorber at (

Reconstruction result based on different interpolation methods (30 measurements, 5% noise).

Ideal image

No interpolation

Linear interpolation

Three cubic interpolations

Cubic spline interpolation

PSO optimized SVM interpolation

The results of 50 measurement points are shown in Figure

Reconstruction performance of different interpolation methods on time reversal algorithm (5% noise).

Time reversal method | MSE (30) | PSNR (30) | TIME (30)/s | MSE (50) | PSNR (50) | TIME (50)/s |
---|---|---|---|---|---|---|

Conventional | 0.3221 | 1.7114 | 0 | 0.1904 | 3.9955 | 0 |

Linear interpolation | 0.1362 | 5.4504 | 0.1097 | 0.0498 | 9.8149 | 0.1091 |

Cubic convolution interpolation | 0.1317 | 5.5954 | 0.0099 | 0.0490 | 9.8876 | 0.0100 |

Cubic spline interpolation | 0.1220 | 5.9287 | 0.0122 | 0.0480 | 9.9752 | 0.0124 |

PSO optimized SVM interpolation | 0.0765 | 7.9569 | 0.4958 | 0.0240 | 12.9815 | 0.4977 |

Reconstruction performance of different interpolation methods on time reversal algorithm (15% noise).

Time reversal method | MSE (30) | PSNR (30) | TIME (30)/s | MSE (50) | PSNR (50) | TIME (50)/s |
---|---|---|---|---|---|---|

Conventional | 0.3230 | 1.7000 | 0 | 0.1913 | 3.9749 | 0 |

Linear interpolation | 0.1384 | 5.3813 | 0.1094 | 0.0522 | 9.6185 | 0.1090 |

Cubic convolution interpolation | 0.1336 | 5.5324 | 0.0101 | 0.0511 | 9.7049 | 0.0105 |

Cubic spline interpolation | 0.1236 | 5.8695 | 0.0121 | 0.0498 | 9.8194 | 0.0123 |

PSO optimized SVM interpolation | 0.0776 | 7.8775 | 0.4978 | 0.0255 | 12.7833 | 0.4979 |

Reconstruction result based on different interpolation methods (50 measurements, 5% noise).

Ideal image

No interpolation

Linear interpolation

Three cubic interpolations

Cubic spline interpolation

PSO optimized SVM interpolation

Comparisons of pressure distribution: (a) small spherical absorber; (b) big spherical absorber.

A tissue phantom is built and shown in Figure

Reconstruction result based on different methods (50 and 100 measurements, 15% noise).

Original image

FBP-50

Conventional-50

PSO-SVM-50

FBP-100

Conventional-100

PSO-SVM-100

In our experiment, the observed sample is 3D polyacrylamide gel (8% acrylamide + 0.5% bisacrylamide) with graphite powder in a standard culture dish (PN: 16235-1SGP, 35 × 12 (mm); diameter: 20 mm). The sample for the optical scanning includes 4 graphite spots (different graphite granule distributions) in different layers. The transducer is one single-element unfocused transducer with 40 MHz center frequency. The image of the sample is shown in Figure

Reconstruction result of PA experiment (50 and 100 measurements).

Image of samples

Conventional-50

PSO-SVM-50

Conventional-100

PSO-SVM-100

In practical photoacoustic imaging, the measurement surface is often incomplete or irregular. When a discrete measured surface is used, the time reversal algorithm fixes the acoustic pressure at these incomplete points which can make them act as optic point scatters, which may scatter back into the imaging region. This can result in arc-like artifacts across the image. One way to reduce the artifacts is to interpolate the measured data to a complete measurement surface acting as the boundary in time reverse course. The PSO optimized SVM interpolation method is used in the time reversal reconstruction algorithm. Compared with other interpolation methods, the method has higher convergence rate and optimization precision. In the course of interpolation, the optimized method can effectively eliminate the phenomenon of contour jaggies and blurring. With better parameter selection, training course, and more measurements, the method can keep more original image details and remove the artifact phenomenon better. In a word, after time reversal reconstruction, both the image magnitude and resolution are improved, so the proposed method can accurately compensate for the effects of acoustic absorption in incomplete photoacoustic imaging.

The primary contribution of this paper is a time reversal algorithm based on PSO optimized SVM interpolation which is proposed to produce more accurate reconstructed PAT images. The proposed method will reduce background interpolation artifacts and blurring in the PAT image at the expense of computational speed. What is more, the algorithm is capable of correcting the attention effect. The effectiveness of the algorithm is verified with the simulation. Also the PSO optimized SVM interpolation based time reversal algorithm can be used for medical PAT imaging system to obtain high resolution.

The authors declared that there is no conflict of interests regarding the publication of this paper.

This research is supported by the National Natural Science Foundation of China (Grants no. 61201307 and no. 61371045) and the Fundamental Research Funds for the Central Universities (Grant no. HIT. NSRIF. 2013132).