Integer lapped transforms and their applications to image coding

This paper proposes new integer approximations of the lapped transforms, called the integer lapped transforms (ILT), and studies their applications to image coding. The ILT are derived from a set of orthogonal sinusoidal transforms having short integer coefficients, which can be implemented with simple integer arithmetic. By employing the same scaling constants in these integer sinusoidal transforms, integer versions of the lapped orthogonal transform (LOT), the lapped biorthogonal transform (LBT), and the hierarchical lapped biorthogonal transform (HLBT) are developed. The ILTs with 5-b integer coefficients are found to have similar coding gain (within 0.06 dB) and image coding performances as their real-valued counterparts. Furthermore, by representing these integer coefficients as sum of powers-of-two coefficients (SOPOT), multiplier-less lapped transforms with very low implementation complexity are obtained. In particular, the implementation of the eight-channel multiplier-less integer LOT (ILOT), LBT (ILBT), and HLBT (IHLBT) require 90 additions and 44 shifts, 98 additions and 59 shifts, and 70 additions and 38 shifts, respectively.