Spline-like Chebyshev polynomial model for compressive imaging

Abstract

This paper introduces a novel spline-like parametric model for an image representation obtained directly from compressive imaging (CI) measurements. As a representation basis we use Chebyshev polynomials. To avoid common problem of blocking artifacts in block-based reconstruction algorithms, a desired number of derivatives are equated on the block boundaries in a spline-like fashion. This introduces a new set of constraints that fits into CI setup. Unlike splines, the proposed system of equations is underdetermined to provide a necessary degree of freedom for achieving sparsity by solving an ℓ1 optimization problem. Recovered coefficients of the parametric model can be further used for image processing where operations can be elegantly defined and calculated. This offers a new framework for acquisition and processing of analog signals without converting them into samples. Experiments on real measurements show that our model achieves sparse representation without visible blocking artifacts from a reduced set of CI measurements.