On using complex homotopy for impulse noise cancellation in images

The area of Compressive Sensing (CS) has been witnessing a flurry of research activity, bringing out solid theoretical results and its usefulness in different applications. With the need to address practicalities, fast reconstruction algorithms are being proposed quite recently. Towards studying their effectiveness in different applications, we have chosen one attractive candidate, the complex homotopy, for CS-based impulse-noise cancellation in images. Compared to popular Compressive Sampling Matching Pursuit (CoSaMP), complex homotopy demonstrated its superiority both in terms of speed of execution and reconstructed image quality. The paper, apart from presenting the supporting results, identifies some useful product codes for the selected application. An attempt is also made towards providing pointers for further examination.