$\ell_{2}$ 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 l
₂
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 l
₂
-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 l
₂
-optimized quantizers. The optimization criterion is to minimize a weighted sum of the l
₂
distortion and the entropy while maintaining a strict l
_∞
error bound. The resulting method obtains good rate-distortion performance in both l
₂
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.