Low-complexity enhanced lapped transform for image coding in JPEG XR / HD photo

JPEG-XR is a new image compression standard that aims at achieving state-of-the-art image compression, while simultaneously keeping the encoder and decoder complexities as low as possible. JPEG-XR is based on Microsoft technology known as HDPHOTO and makes use of a block-transform. This transform, known as Lapped Biorthogonal Transform (LBT), requires only a small memory footprint while providing the compression benefits of a larger block transform. In this work, we propose to replace the LBT by a representation in Legendre orthogonal polynomial basis. The motivation behind using the Legendre polynomials is that, in general, moment functions of orthogonal polynomials provide better feature representations over other type of moments and have some properties related to the human visual system (HVS). However, Legendre polynomials have a unit weight function and recurrence relation involving real coefficients, which make them suitable for defining image representation. We show that the expansion in Legendre polynomial basis can be implemented via lifting operations and has the same computation complexity as the LBT. The experimental evaluation of our modified JPEG-XR scheme shows beneficial improvements in terms of visual quality over the standard JPEG-XR.