Legendre polynomials in signal reconstruction and compression

In this paper, we present a method for signal reconstruction using orthogonal transform based on discrete Legendre polynomials. Using such a transform provides computational advantages over polynomial basis. We extend the discrete Legendre polynomials to two-dimensional discrete Legendre polynomials for reconstructing and compressing an image. In the applications, we notice that when the order of a polynomial becomes large, the proposed method tends to exhibit numerical instabilities. We bring forward a possible way to avoid such instabilities. Simulation results illustrate that the error resulted from compression is usually low with a satisfactory compression ratio by using the proposed method. An application in system identification is also presented.