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.

JPEG is an international standard for still image compression. The JPEG baseline algorithm allows users to supply the custom quantization table and Huffman table to control the compression ratio and the quality of the encoded image. Methods for determining the quantization matrix are usually based on (i) rate-distortion theory and (ii) spatial masking effects of the human visual system. Wu and Gersho (1993) proposed a recursive algorithm for generating picture-adaptive quantization tables based on rate-distortion approach but the complexity of the encoding algorithm is rather high. In this paper, we propose improvements to the Wu-Gersho's algorithm and a new bit allocation algorithm. Simulation results show that our new algorithm is superior to the Wu-Gersho's algorithm in terms of speed and peak signal to noise ratio (PSNR). Moreover, by incorporating the human visual system (HVS), our proposed coder can encode images with better visual quality.