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Photoacoustic imaging is an emerging noninvasive imaging technique with great potential for a wide range of biomedical imaging applications. However, with few-view data the filtered back-projection method will create streak artifacts. In this study, the regularized iterative weighted filtered back-projection method was applied to our photoacoustic imaging of the optical absorption in phantom from few-view data. This method is based on iterative application of a nonexact 2DFBP. By adding a regularization operation in the iterative loop, the streak artifacts have been reduced to a great extent and the convergence properties of the iterative scheme have been improved. Results of numerical simulations demonstrated that the proposed method was superior to the iterative FBP method in terms of both accuracy and robustness to noise. The quantitative image evaluation studies have shown that the proposed method outperforms conventional iterative methods.

Photoacoustic imaging (PAI) combining good acoustic resolution with high optical contrast in a single modality has great potential for tremendous clinical applications [

Analytic algorithms like filtered back-projection (FBP) and time-reversal based reconstruction attain very fast reconstruction performance [

In this study, inspired by the iterative weighted approaches in CT [

This paper is organized as follows. In Section

According to the forward problem for an acoustically homogeneous model present in [

Iterative improved FBP (IFBP) methods have been used to reduce artifacts due to an insufficient data and streaks due to missing angles. The update step of IFBP is then given by [

In this section, we will present the RIWFBP method for the few-view PAI imaging. This contribution is an extension of theory and experiments on iterative weighted FBP (IWFBP) presented in [

During the reconstruction, we firstly used ^{2} neighborhood. The last term is obviously a penalty term. The minimization of (

Computer simulations were conducted to demonstrate the effectiveness of the proposed method. The imaged source with a size of 256 × 256 pixels, as shown in Figure

Images reconstructed from simulated data corresponding to the numerical phantom (a). (b) 30 detectors over 90°, using IFBP. (c) 60 detectors over 180°, using IFBP. (d) 120 detectors over 360°, using RIWFBP. (e) 30 detectors over 90°, using RIWFBP. (f) 60 detectors over 180°, using RIWFBP.

Images reconstructed with the IFBP method and the RIWFBP method from few-view data are displayed in Figure

Figures

Photoacoustic imaging of the numerical phantom using 60 detections over 180°. (a) IFBP; (b) IWFBP; (c) RIWFBP. (d) Reconstruction normalized mean absolute error from 180° under different number of iterations.

Reconstruction errors between the original image and the reconstructed images were calculated and shown in Figure

To study the robustness of the RIWFBP method, Gaussian noises with SNR 40, 30, and 20 were added to the signals. Figure

Reconstruction normalized mean absolute errors from 180° with a different detector number. (a) Noiseless observation; noisy observation with (b) SNR = 40 dB; (c) SNR = 30 dB; (d) SNR = 20 dB.

In the phantom experiment, the RIWFBP method was tested and evaluated. For comparative purposes, reconstruction results of the FBP method and the IFBP method are also presented. Two graphite rods with a diameter

Reconstructed images based on few-view data. (a) 60 detectors over 180°, with FBP. The insert at the top-left corner is the photograph of the phantom. (b) 60 detectors over 180°, with IFBP. (c) 60 detectors over 180°, with RIWFBP.

The sample was irradiated with pulses from a Q-switched Nd: YAG Laser. The pulse duration was 7.5 ns and the pulse repetition rate was 10 Hz. A focused hydrophone (Precision Acoustics Ltd.) with frequency response of 5 MHz was controlled by a high precision stepping motor to scan around the phantom in a circular manner for photoacoustic signal acquisition. The distance between the transducer and the rotation center was 45 mm. The induced photoacoustic waves were captured at 60 positions over 180°. At each position 50 signals were averaged. In real experiments, we did not know the true image, so the iterative stop criteria,

Figures

In this work, the RIWFBP method has been applied to reconstruct photoacoustic images with few-view data. From the experiments we conclude that during the first five iterations, the RIWFBP method efficiently suppresses strips artifacts produced by IWFBP over 180°. The NMAE calculation also denoted that the RIWFBP method has an advantage in accuracy compared with other test methods. With regularization, the proposed method reaches the final solution faster than without. It is therefore easier to decide when to terminate the iterative loop. The application of the RIWFBP method will significantly reduce the number of ultrasound transducers and scanning time needed for high quality photoacoustic image reconstruction. Therefore, it can be a promising candidate for resolving the few-view PAI problem.

The authors declare that they have no competing interests.

This paper is supported by the National Natural Science Foundation of China under Grant nos. 31271065, 61300154, and 61402215, the Natural Science Foundation of Shandong Province under Grant nos. 2014ZRB019VC and 2014ZRB019E0, and the Doctoral Fund of Liaocheng University under Grant no. 318051304.