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This paper presents a novel technique based on Compressive Sensing (CS) for canceling impulse noise in images. The technique is pivoted around exploiting the strong connection between CS and error correction using the complex (or real) field codes. Even though the usage of real field Bose-Chaudhuri-Hocquenghem (BCH) codes for impulse noise cancellation in images is rather old, bringing the CS framework to address this classical problem in image processing provides a fresh perspective. Specifically, the paper investigates a CS-based product code based on partial Fourier matrices, with the requisite rows chosen based on a Perfect Difference Set (PDS) or consecutively. The decoding algorithms are based on the CS reconstruction and are rather elegant and computationally efficient compared to those considered earlier for real BCH codes. Extensive simulation studies suggest that the novel PDS-based product code is effective in canceling the impulse noise through iterative decoding.