光學解析度光聲顯微鏡雖透過光學聚焦而擁有高度橫向解析度，但卻受限於較差的軸向解析度，其軸向解析度通常較橫向解析度差一個數量級。光學解析度光聲顯微鏡的軸向解析度主要由超音波接收器的頻寬大小決定。超高頻 (大於100 MHz)的超音波探頭搭配維納濾波器(Wiener filter)反折積近來已被提出以取得相同的橫向與軸向空間解析度，但因高頻的光聲訊號在組織中衰減快速反而使穿透深度受限。在此論文中我們提出了一個基於凸優化的反折積方法，此方法提升了光學解析度光聲顯微鏡的軸向解析度，並且不需要實際地增加超音波探頭的頻寬。基於光吸收子的稀疏分佈、非負實數的能量累積、以及雷射光的強聚焦等光學解析度光聲顯微鏡的主要特性，我們衍生出一些條件式，並將這些條件加入我們提出的方法之中。使用25 MHz的超音波探頭在訊雜比率為20 dB的環境之下，我們所提出的方法遠優於傳統的維納濾波器及理查森露西(Richardson-Lucy)演算法，提供了軸向解析度約4.9倍的改善(14.4 um vs. 70 um)，且提升了訊雜比。此外，我們更透過血液抹片成像及活體鼠耳的微細血管成像來進一步驗證我們所提出的方法。

Optical resolution photoacoustic microscopy (OR-PAM), though possessing high lateral resolution via optical focusing, has been limited by its poor axial resolution, which typically is an order of magnitude worse than the lateral resolution. Its axial resolution mainly depends on the bandwidth of the acoustic detection. To form images with isometric spatial resolution, ultrahigh frequency detectors larger than 100 MHz along with a Wiener deconvolution method have been employed, yet suffering severe high-frequency attenuation and thus limited imaging depth and working distance. In this study, we propose a convex-optimization based deconvolution method to improve the axial resolution of OR-PAM without physically increasing the detection bandwidth. OR-PAM properties – sparsity of absorber distribution, non-negative optical energy deposition, and optical focusing are leveraged as constraints in the proposed method. With 20-dB system signal-to-noise ratio (SNR), the proposed method experimentally outperformed the conventional Wiener and Richardson-Lucy deconvolution algorithms, providing about 4.9-fold finer axial resolution (14.4 um vs. 70 um) and improved SNR for a 25-MHz detector in blood smear. In addition, the improvement achieved with the proposed method was demonstrated by imaging blood smears and microvasculature of mouse ear in vivo.

摘要 i
Abstract ii
Contents iii
List of Figures v
List of Tables viii
Chapter 1 Introduction 1
1.1 Photoacoustic Microscopy 1
1.2 Optical-Resolution Photoacoustic Microscopy (OR-PAM) 2
1.3 Motivation 4
Chapter 2 A-line Signal Model of Optical Resolution Photoacoustic Microscopy 7
2.1 Laser Pulse Length 7
2.2 Electrical Impulse Response 7
2.3 Spatial Impulse Response 8
2.4 System Characteristics of OR-PAM 10
2.5 A-line Signal System Model 10
2.6 Proposed Method 14
2.6.1 Threshold in L1-norm 16
Chapter 3 Simulations and Experiments 19
3.1 Simulations 19
3.1.1 Parameters and Scheme 19
3.1.2 Maximum Achievable Resolution 21
3.1.3 Effect of Model Error on Bandwidth 23
3.1.4 Maintenance of Relative Absorption Ratio 25
3.2 Experiments 27
3.2.1 Experimental system 27
3.2.2 Algorithm Verification 28
3.2.3 Blood Smear Imaging 33
3.2.4 Vasculature Imaging of Mouse Ear 35
3.2.5 Effect of Deconvolution in Lateral Direction 36
Chapter 4 Conclusions and Future Work 39
4.1 Conclusions 39
4.2 Future Work 41
References 42

[1] Jianhua Chen, Riqiang Lin, Huina Wang, Jing Meng, Hairong Zheng, and Liang Song, “Blind-deconvolution Optical-resolution Photoacoustic Microscopy in Vivo,” Optics express 21(6), 7316-7327 (2013).
[2] Hao F Zhang, Konstantin Maslov, George Stoica, and Lihong V Wang, "Functional photoacoustic Microscopy for High-resolution and Noninvasive in Vivo Imaging," Nature biotechnology 24(7), 848-851 (2006).
[3] Jignesh Shah, Suhyun Park, Salavat Aglyamov, Timothy Larson, Li Ma, Konstantin Sokolov, Keith Johnston, and Thomas Milner, and Stanislav Y. Emelianov, “Photoacoustic Imaging and Temperature Measurement for Photothermal Cancer Therapy,” Journal of biomedical optics 13(3), 034024-034024 (2008).
[4] Lidai Wang, Konstantin Maslov, and Lihong V. Wang, “Single-cell Label-free Photoacoustic Flowoxigraphy in Vivo,” Proceedings of the National Academy of Sciences 110(15), 5759-5764 (2013).
[5] Chi Zhang, Konstantin Maslov, and Lihong V. Wang, “Subwavelength-resolution Label-free Photoacoustic Microscopy of Optical Absorption in Vivo,” Optics letters 35(19), 3195-3197 (2010).
[6] Chi Zhang, Konstantin Maslov, Song Hu, Ruimin Chen, Qifa Zhou, K.Kirk Shung, and Lihong V. Wang, “Reflection-mode Submicron-resolution in Vivo Photoacoustic Microscopy,” Journal of biomedical optics 17(2), 0205011-0205014 (2012).
[7] Chi Zhang, Konstantin Maslov, Junjie Yao, and Lihong V. Wang, “In Vivo Photoacoustic Microscopy with 7.6-um Axial Resolution using a Commercial 125-MHz Ultrasonic Transducer,” Journal of Biomedical Optics 17(11), 116016-116016 (2012).
[8] C. Zhang, C. Li, and L. V. Wang, “Fast and Robust Deconvolution-Based Image Reconstruction for Photoacoustic Tomography in Circular Geometry: Experimental Validation,” Photonics Journal, IEEE 2(1), 57-66 (2010).
[9] L. V. Wang and S. Hu, “Photoacoustic Tomography: in Vivo Imaging from Organelles to Organs,” Science 335, 1458–1462 (2012).
[10] Hao Li, Biqin Dong, Zhen Zhang, Hao F. Zhang, and Cheng Sun, “A Transparent Broadband Ultrasonic Detector Based on an Optical Micro-ring Resonator for Photoacoustic Microscopy,” Scientific reports 4 (2014).
[11] Jing Meng, Lihong V. Wang, Dong Liang, and Liang Song, “In vivo Optical-resolution Photoacoustic Computed Tomography with Compressed Sensing,” Optics letters 37(22), 4573-4575 (2012).
[12] Jing Meng, Lihong V. Wang, Leslie Ying, Dong Liang, and Liang Song, “Compressed-sensing Photoacoustic Computed Tomography in Vivo with Partially Known Support,” Optics Express 20(15), 16510-16523 (2012).
[13] G.Dougherty, and Z.Kawaf, “The Point Spread Function Revisited: Image Restoration using 2-D Deconvolution,” Radiography 7(4), 255-262 (2001).
[14] Nicolas Dey, Laure Blanc-Feraud, Christophe Zimmer, Pascal Roux, Zvi Kam, Jean-Christophe Olivo-Marin, and Josiane Zerubia, “Richardson-Lucy Algorithm with Total Variation Regularization for 3D Confocal Microscope Deconvolution,” Microscopy research and technique 69(4), 260-266 (2006).
[15] Jensen, and John, “A New Approach to Calculating Spatial Impulse Responses,” Ultrasonics Symposium, 1997. Proceedings, 1997 IEEE 2, 1755-1759 (1997).
[16] Jing Meng, Chengbo Liu, Jiaxiang Zheng, Riqiang Lin, and Liang Song, “Compressed Sensing Based Virtual-detector Photoacoustic Microscopy in Vivo,” Journal of biomedical optics 13(3), 036003-036003 (2014).
[17] Liren Zhu, Lei Li, Liang Gao, and Lihong V. Wang, “Multiview Optical Resolution Photoacoustic Microscopy,” Optica 1(4), 217-222 (2014).
[18] Christoph Dalitz, Regina Pohle-Frohlich, and Thorsten Michalk, “Point Spread Functions and Deconvolution of Ultrasonic Images,” Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions 62(3), 531-544 (2015).
[19] Suiren Wan, Balasundar I. Raju, and Mandayam A. Srinivasan, “Robust Deconvolution of High-Frequency Ultrasound Images Using Higher-Order Spectral Analysis and Wavelets,” Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions 50(10), 1286-1295 (2003).
[20] Meng-Lin Li, Yi-Chieh Tseng, and Chung-Chih Cheng, “Model-based Correction of Finite Aperture Effect in Photoacoustic Tomography,” Optics express 18(25), 26285-26292 (2010).
[21] Haiteng Wu, Jian Chen, Shiwei Wu, Haoran Jin and Keji Yang, “A Model-based Regularized Inverse Method for Ultrasonic B-scan Image Reconstruction,” Measurement Science and Technology 26(10), 105401 (2015).
[22] Junjie Yao, Konstantin I. Maslov, Yu Zhang, Younan Xia, and Lihong V. Wang, “Label-free Oxygen-metabolic Photoacoustic Microscopy in Vivo,” Journal of biomedical optics 16(7), 076003-076003 (2011).
[23] Zhixing Xie, Sung-Liang Chen, Tao Ling, L. Jay Guo, Paul L. Carson, and Xueding Wang, “Pure Optical Photoacoustic Microscopy,” Optics express 19(10), 9027-9034 (2011).
[24] D. Kundur and D. Hatzinakos, “Blind Image Deconvolution,” IEEE Signal Processing Mag 13(3), 43-64 (1996).
[25] Chengpu Yu, Cishen Zhang, and Lihua Xie, “A Blind Deconvolution Approach to ultrasound imaging,” Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transaction 59(2), 271-280 (2012).
[26] M. A. Sapia, M. D. Fox, L. M. Loew, and J. C. Schaff, “Ultrasound Image Deconvolution using Adaptive Inverse Filtering,” Computer-Based Medical Systems, Proceedings, 12th IEEE Symposium, 248-253 (1999).
[27] Ramesh Neelamani, Hyeokho Choi, and Richard Baraniuk, “ForWaRD: Fourier-wavelet Regularized Deconvolution for Ill-conditioned Systems,” Signal Processing, IEEE Transaction 52(2), 418-433 (2004).
[28] Michael Grant and Stephen Boyd. CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx, September 2013.
[29] Michael Grant and Stephen Boyd. Graph implementations for nonsmooth convex programs, Recent Advances in Learning and Control (a tribute to M. Vidyasagar), V. Blondel, S. Boyd, and H. Kimura, editors, pages 95-110, Lecture Notes in Control and Information Sciences, Springer, 2008. http://stanford.edu/~boyd/graph_dcp.html.
[30] J.A. Jensen: Field: A Program for Simulating Ultrasound Systems, Paper presented at the 10th Nordic-Baltic Conference on Biomedical Imaging Published in Medical & Biological Engineering & Computing, pp. 351-353, Volume 34, Supplement 1, Part 1, 1996.
[31] J.A. Jensen and N. B. Svendsen: Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers, IEEE Trans. Ultrason., Ferroelec., Freq. Contr., 39, pp. 262-267, 1992.