A gradient descent sparse adaptive matching pursuit algorithm based on compressive sensing

Aiming at the problem of original signal reconstruction based on one-dimensional (1D) compressive sensing (CS), a gradient descent sparse adaptive matching pursuit (GDSAMP) algorithm is proposed for 1D sparse signal. By setting the augmented lagrange function, the process of signal reconstruction is transformed to the unconstrained optimization problem. The iteration procedure of algorithm includes three steps: the gradient descent searching based on total deviations of one-order and two-order, the adaptive cutting on sparse coefficients and the improvement of least square projection. Based on the above steps, an algorithm framework is designed for recognizing and locating sub-pattern signal on large signal sets. Experimental results show that the GDSAMP algorithm has better efficiency on reconstructing original signal. At the same time, it can quickly locate the matching interval of sub-pattern signal on large signal sets. The researching results can be used in signal retrieval, voice recognition, image recognition and computer vision, ... etc.