Van de Sompel Dominique, Sasportas Laura S, Jokerst Jesse V, Gambhir Sanjiv S
Molecular Imaging Program at Stanford (MIPS), Stanford University School of Medicine, Stanford University, Stanford, CA 94305, United States of America.
Department of NanoEngineering, UC San Diego, La Jolla, CA 92093, United States of America.
PLoS One. 2016 Mar 31;11(3):e0152597. doi: 10.1371/journal.pone.0152597. eCollection 2016.
In this work, we compare the merits of three temporal data deconvolution methods for use in the filtered backprojection algorithm for photoacoustic tomography (PAT). We evaluate the standard Fourier division technique, the Wiener deconvolution filter, and a Tikhonov L-2 norm regularized matrix inversion method. Our experiments were carried out on subjects of various appearances, namely a pencil lead, two man-made phantoms, an in vivo subcutaneous mouse tumor model, and a perfused and excised mouse brain. All subjects were scanned using an imaging system with a rotatable hemispherical bowl, into which 128 ultrasound transducer elements were embedded in a spiral pattern. We characterized the frequency response of each deconvolution method, compared the final image quality achieved by each deconvolution technique, and evaluated each method's robustness to noise. The frequency response was quantified by measuring the accuracy with which each filter recovered the ideal flat frequency spectrum of an experimentally measured impulse response. Image quality under the various scenarios was quantified by computing noise versus resolution curves for a point source phantom, as well as the full width at half maximum (FWHM) and contrast-to-noise ratio (CNR) of selected image features such as dots and linear structures in additional imaging subjects. It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise. While the Wiener filter achieved a similar image resolution, it tended to underrepresent the lower frequency content of the deconvolved signals, and hence of the reconstructed images after backprojection. In addition, its robustness to noise was poorer than that of the Tikhonov filter. The performance of the Fourier filter was found to be the poorest of all three methods, based on the reconstructed images' lowest resolution (blurriest appearance), generally lowest contrast-to-noise ratio, and lowest robustness to noise. Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.
在这项工作中，我们比较了三种时间数据反卷积方法在光声层析成像（PAT）的滤波反投影算法中的优点。我们评估了标准傅里叶除法技术、维纳反卷积滤波器和蒂霍诺夫L - 2范数正则化矩阵求逆方法。我们在各种外观的对象上进行了实验，即一根铅笔芯、两个人造体模、一个体内皮下小鼠肿瘤模型以及一个灌注并切除的小鼠大脑。所有对象均使用带有可旋转半球形碗的成像系统进行扫描，128个超声换能器元件以螺旋模式嵌入其中。我们表征了每种反卷积方法的频率响应，比较了每种反卷积技术实现的最终图像质量，并评估了每种方法对噪声的鲁棒性。通过测量每个滤波器恢复实验测量脉冲响应的理想平坦频谱的准确度来量化频率响应。通过计算点源体模的噪声与分辨率曲线以及其他成像对象中选定图像特征（如点和线性结构）的半高宽（FWHM）和对比度噪声比（CNR）来量化各种场景下的图像质量。结果发现，蒂霍诺夫滤波器在低频和高频成分之间实现了最精确的平衡（通过将反卷积脉冲响应信号的频谱与理想平坦频谱进行比较来衡量），实现了具有竞争力的图像分辨率和对比度噪声比，并且对噪声具有最大的鲁棒性。虽然维纳滤波器实现了类似的图像分辨率，但它往往低估了反卷积信号的低频成分，从而也低估了反投影后重建图像的低频成分。此外，它对噪声的鲁棒性比蒂霍诺夫滤波器差。基于重建图像的最低分辨率（最模糊的外观）、通常最低的对比度噪声比以及最低的噪声鲁棒性，发现傅里叶滤波器的性能在所有三种方法中是最差的。总体而言，蒂霍诺夫滤波器被认为能产生最理想的图像重建结果。
