Orthogonal gradient measurement matrix optimisation method

The optimisation of measurement matrix that is within the compressive sensing framework is considered in this study. Based on the fact that an information factor with smaller mutual coherence performs better, the gradient measurement matrix optimisation method is improved by an orthogonal search direction revision factor. This algorithm updates the approximation of ideal Gram matrix of information operator and the measurement matrix alternatingly. Using measurement matrix and sparse basis to represent the Gram matrix, the measurement matrix is optimised by the gradient algorithm, in which an orthogonal gradient search direction revision factor is proposed and utilised to further improve the performance of measurement matrix. This orthogonal factor is computed by the Cayley transform of a real skew symmetric matrix that is related to the gradient and the measurement matrix. Results of several experiments show that compared with the initial random matrix, the optimised measurement matrix can lead to better signal reconstruction quality.