Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Algorithm 820: A flexible implementation of matching pursuit for Gabor functions on the interval
ACM Transactions on Mathematical Software (TOMS)
IEEE Transactions on Information Theory
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Scanning acoustic microscopy is an imaging method in which the focused high frequency ultrasound is used to visualize the micro structures. The morphology and acoustic properties of the biological tissues can be evaluated using scanning acoustic microscope system. To determine thin tissues having micrometer thickness, the high acoustic frequency is required for conventional SAM. In practice the acoustic frequency is restricted by the penetration depth through the material. Characterization of thin sliced tissue is difficult, as the reflected signals from top and bottom are superimposed. In order to improve the axial resolution of conventional SAM, a technique based on sparse signal representation in overcomplete time---frequency dictionaries is investigated and among the great number of algorithms for finding sparse representation, we first apply matching pursuit (MP) and basis pursuit (BP) and then propose the orthogonal matching pursuit (OMP) and stagewise orthogonal matching pursuit (StOMP) algorithms to decompose the A-scan signal to an overcomplete Gabor dictionary. Different criteria are used for measuring the performance of these algorithms in C-scan imaging. The proposed method can separate closely space overlapping echoes beyond the resolution of conventional SAM systems and also the final results show that StOMP performs best overall in extracting the specific echo, since this algorithm is precise and fast.