# $\ell_{2}$ Optimized Predictive Image Coding With $\ell_{\infty}$ Bound Academic Article

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### abstract

• In many scientific, medical, and defense applications of image/video compression, an [Symbol: see text]∞ error bound is required. However, pure[Symbol: see text]∞-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 [Symbol: see text]∞-based image coding methods suffer from poor rate control. In contrast, the [Symbol: see text]2 error metric aims for average fidelity and hence preserves the subtlety of smooth waveforms better than the ∞ error metric and it offers fine granularity in rate control, but pure [Symbol: see text]2-based image coding methods (e.g., JPEG 2000) cannot bound individual errors as the [Symbol: see text]∞-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 [Symbol: see text]2-optimized quantizers. The optimization criterion is to minimize a weighted sum of the [Symbol: see text]2 distortion and the entropy while maintaining a strict [Symbol: see text]∞ error bound. The resulting method obtains good rate-distortion performance in both [Symbol: see text]2 and [Symbol: see text]∞ metrics and also increases the rate granularity. Compared with JPEG 2000, the new method not only guarantees lower [Symbol: see text]∞ error for all bit rates, but also it achieves higher PSNR for relatively high bit rates.

### publication date

• December 2013