Distributed Compressive Sensing Algorithm for Photoacoustic Tomography

Biomedical imaging techniques are playing an essential role in diagnosing different kinds of diseases, which always motivates the search for improving their sensitivity and accuracy. Photoacoustic Tomography (PAT) is one of the most powerful techniques. PAT has many advantages as it is less expensive and faster than Magnetic Resonance Imaging (MRI). It combines the advantages of optical imaging and ultrasound imaging as it provides high contrast, high penetration, and high-resolution images for biological tissues. Also, it uses non-ionizing radiation which is very safe for human health. The main challenge in PAT is that human tissues can be exposed only to a limited amount of radiation, so a full-view of PAT requires many transducers and a great number of measurements. This thesis aims to develop an efficient reconstruction algorithm of Photoacoustic (PA) images that uses a few number of transducers, a few number of measurements, and offers low computational complexity while maintaining a high quality of recovered images. The proposed reconstruction algorithm depends on the Compressive Sensing (CS) theory which is a signal processing technique that is capable of forming a full view PAT images (under certain prerequisites) with a few number of measurements. The proposed algorithm solves the CS problem using a distributed and parallel implementation of the Alternating Direction Method of Multipliers (ADMM). ADMM is a well-known method for solving convex optimization problems. A group of local processors that work in parallel with one global processor is used to form the images. The iterative algorithm of ADMM is distributed over local processors in such a way perfect reconstruction of images is possible. Simulation results show that the proposed algorithm is powerful and successful in reconstructing different kinds of PA images with very high quality and significantly reduced computational complexity. Reducing the computational complexity is reflected in a much lower reconstruction time. Also, the algorithm requires lower cost and shorter acquisition time since the CS theory is used which allows the recovery of images from a few number of samples and sensors. Although the idea of distributed ADMM has been introduced before in literature but to the best of our knowledge, this is the first work to apply distributed ADMM method in recovering photoacoustic images by distributing the iterative algorithm among multiple processors working in parallel

A simple and accurate matrix for model based photoacoustic imaging

Accurate model-based methods in Photo-Acoustic Tomography (PAT) can reconstruct the image from insufficient and inaccurate measurements. Most of the models either make the simplified assumption of spherical averaging or use accurate models that have computationally burdensome implementations. We present a simple and accurate measurement matrix that is derived from the pseudo-spectral PAT model. The accuracy of the measurement matrix is first validated against the experimental PAT signal. We also compare the model against the standard k-wave measurement model and the spherical averaging model. We then highlight several reconstruction strategies based on the nature of the region of interest to further demonstrate the accuracy of the proposed measurement matrix