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Recently, many types of compressive sensing (CS) matrices have been constructed. Most of these constructions focus on the measurement of one-dimensional (1-D) signals. However, many practical applications involve the acquisition of two-dimensional (2-D) signals. One of the main difficulties in the direct application of a 1-D CS measurement system to the measurement of a 2-D signal is that the computational complexity and data storage increase sharply with increasing dimension. For the measurement of 2-D signals, the structures of block CS (BCS) and Kronecker CS (KCS) have been presented. By exploiting the sparsity of 2-D signals, we provide a new extended 2-D separable measurement structure in this work, which implements separate linear operations along each 2-D signal dimension. The new structure extends the traditional 2-D separable measurement operator via measuring each subset of the signal by different CS operators, and BCS and KCS can be unified into this structure. The lower bound of the restricted isometry constant of the extended 2-D separable matrix is identified. Simulation results demonstrate the validity of our proposed structure. The proposed structure reduces the complexity of implementation and storage, and provides a new construction for the measurement of 2-D sparse signals. [ABSTRACT FROM AUTHOR]

A number of tree search based methods have recently been utilized for compressive sensing signal reconstruction. Among these methods, a heuristic algorithm named A* orthogonal matching pursuit (A*OMP) follows best-first search principle and employs dynamic cost model which makes sparse reconstruction exceptionally excellent. Since the algorithm performance of A*OMP relies heavily on preset parameters in the cost model and the estimation of these preset parameters requires a large number of experiments, there is room for improvement in A*OMP. In this paper, an improved algorithm referred to as Nonlinear Regression A*OMP (NR-A*OMP) is proposed which is built on the residue trend to avoid the estimation procedure. This method is inspired by the fact that the residue is correlated closely to the measurement matrix. The residue trend reflects the characteristics of nonlinear regression with the increasing of sparsity K . In addition, restricted isometry property (RIP) based general conditions are introduced to ensure the effectiveness and practicality of the algorithm. Numerical simulations demonstrate the superiority of NR-A*OMP in both reconstruction rate and normalized mean squared error. Results indicate that the performance of NR-A*OMP can become nearly equal to or even better than that of A*OMP with perfect preset parameters. [ABSTRACT FROM AUTHOR]