The Application of Compressed Sensing for

Photo-acoustic (PA) imaging has been developed for different purposes, but recently, the modality has gained interest with applications to small animal imaging. As a technique it is sensitive to endogenous optical contrast present in tissues and, contrary to diffuse optical imaging, it promises to bring high reso- lution imaging for in vivo studies at midrange depths (3-10 mm). Because of the limited amount of radiation tissues can be exposed to, existing reconstruction algorithms for circular tomography require a great number of measurements and averaging, implying long acquisition times. Time-resolved PA imaging is therefore possible only at the cost of complex and expensive electronics. This paper suggests a new reconstruction strategy using the compressed sensing formalism which states that a small number of linear projections of a compressible image contain enough information for reconstruction. By directly sampling the image to recover in a sparse representation, it is possible to dramatically reduce the number of measurements needed for a given quality of reconstruction.

[1]  R. Kruger,et al.  Photoacoustic ultrasound (PAUS)--reconstruction tomography. , 1995, Medical physics.

[2]  K. P. Köstli,et al.  Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response. , 2003, Applied optics.

[3]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[4]  Lihong V. Wang,et al.  Photoacoustic imaging of lacZ gene expression in vivo. , 2007, Journal of biomedical optics.

[5]  M. R. Osborne,et al.  On the LASSO and its Dual , 2000 .

[6]  D. Donoho Nonlinear Solution of Linear Inverse Problems by Wavelet–Vaguelette Decomposition , 1995 .

[7]  Robert A Kruger,et al.  Thermoacoustic molecular imaging of small animals. , 2003, Molecular imaging.

[8]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[9]  Lihong V. Wang,et al.  Improved in vivo photoacoustic microscopy based on a virtual-detector concept. , 2006, Optics letters.

[10]  Yaakov Tsaig,et al.  Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse , 2008, IEEE Transactions on Information Theory.

[11]  Minghua Xu,et al.  Time-domain reconstruction for thermoacoustic tomography in a spherical geometry , 2002, IEEE Transactions on Medical Imaging.

[12]  Minghua Xu,et al.  Photoacoustic tomography of biological tissues with high cross-section resolution: reconstruction and experiment. , 2002, Medical physics.

[13]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

[14]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[15]  Hao Zhang,et al.  Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy , 2007 .

[16]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[17]  Alexander A. Oraevsky,et al.  Optoacoustic imaging of blood for visualization and diagnostics of breast cancer , 2002, SPIE BiOS.

[18]  Geng Ku,et al.  Imaging of tumor angiogenesis in rat brains in vivo by photoacoustic tomography. , 2005, Applied optics.

[19]  E. Candès,et al.  New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities , 2004 .

[20]  Geng Ku,et al.  Deeply penetrating photoacoustic tomography in biological tissues enhanced with an optical contrast agent. , 2005, Optics letters.

[21]  Lihong V. Wang,et al.  Biomedical Optics: Principles and Imaging , 2007 .

[22]  S. Mallat,et al.  Adaptive greedy approximations , 1997 .

[23]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[24]  D. Donoho For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution , 2006 .

[25]  Justin Romberg,et al.  Practical Signal Recovery from Random Projections , 2005 .

[26]  Lihong V. Wang,et al.  Universal back-projection algorithm for photoacoustic computed tomography. , 2005 .