$\ell _{2}$ Optimized Predictive Image Coding With $\ell _{\infty }$ Bound

In many scientific, medical, and defense applications of image/video compression, an l_∞ error bound is required. However, pure l_∞-optimized image coding, colloquially known as near-lossless image coding, is prone to structured errors such as contours and speckles if the bit rate is not sufficiently high; moreover, most of the previous l_∞-based image coding methods suffer from poor rate control. In contrast, the l₂ error metric aims for average fidelity and hence preserves the subtlety of smooth waveforms better than the l∞ error metric and it offers fine granularity in rate control, but pure l₂-based image coding methods (e.g., JPEG 2000) cannot bound individual errors as the l_∞-based methods can. This paper presents a new compression approach to retain the benefits and circumvent the pitfalls of the two error metrics. A common approach of near-lossless image coding is to embed into a DPCM prediction loop a uniform scalar quantizer of residual errors. The said uniform scalar quantizer is replaced, in the proposed new approach, by a set of context-based l₂-optimized quantizers. The optimization criterion is to minimize a weighted sum of the l₂ distortion and the entropy while maintaining a strict l_∞ error bound. The resulting method obtains good rate-distortion performance in both l₂ and l_∞ metrics and also increases the rate granularity. Compared with JPEG 2000, the new method not only guarantees lower l_∞ error for all bit rates, but also it achieves higher PSNR for relatively high bit rates.