A gradient-based approach to optimization of compressed sensing systems

This paper deals with a gradient-based approach to optimizing compressed sensing systems. An alternative measure is proposed for incoherent sparsifying dictionary design. An iterative procedure is developed for searching the optimal dictionary, in which the dictionary update is executed using a gradient descent-based algorithm. The optimal sensing matrix problem is investigated in terms of minimizing ∥H−G∥F2, where H is the target of Gram matrix of desired coherence property. Unlike the traditional approaches, G is taken as the Gram of the normalized equivalent dictionary of the system, ensuring that ∥H−G∥F2 has the designated physical meaning. A gradient descent-based algorithm is derived for solving the optimal sensing matrix problem. The validity of the proposed approaches is confirmed with experiments carried out using synthetic data and real images.