Avoidance of singular point in reversible KLT

In this report, permutation of order and sign of signals are introduced to avoid singular point problem of a reversible transform. When a transform is implemented in the lifting structure, it can be "reversible" in spite of rounding operations inside the transform. Therefore it has been applied to lossless coding of digital signals. However some coefficient values of the transform have singular points (SP). Around the SP, rounding errors are magnified to huge amount and the coding efficiency is decreased. In this report, we analyze the SP of a three point KLT for RGB color components of an image signal, and introduce permutation of order and sign of signals to avoid the SP problem. It was experimentally confirmed that the proposed method improved PSNR by approximately 15 [dB] comparing to the worst case.