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Compressive sensing (CS) makes it possible to more naturally create compact representations of data with respect to a desired data rate. Through wavelet decomposition, smooth and piecewise smooth signals can be represented as sparse and compressible coefficients. These coefficients can then be effectively compressed via the CS. Since a wavelet transform divides image information into layered blockwise wavelet coefficients over spatial and frequency domains, visual improvement can be attained by an appropriate perceptually weighted CS scheme. We introduce such a method in this paper and compare it with the conventional CS. The resulting visual CS model is shown to deliver improved visual reconstructions.