The Nonnegative Zero-Norm Minimization Under Generalized Z-Matrix Measurement

In this paper, we consider the zero-norm minimization problem with linear equation and nonnegativity constraints. By introducing the concept of generalized Z-matrix for a rectangular matrix, we show that this zero-norm minimization with such a kind of measurement matrices and nonnegative observations can be exactly solved via the corresponding p-norm minimization with p in the open interval from zero to one. Moreover, the lower bound of sample number for exact recovery is allowed to be the same as the sparsity of the original image or signal by the underlying zero-norm minimization. A practical application in communications is presented, which satisfies the generalized Z-matrix recovery condition.