Sigma Delta Quantization for Images
Sigma Delta Quantization for Images
复制标题
图像的 Sigma Delta 量化
DOI：
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发表时间：
2020
影响因子：
3
通讯作者：
Rongrong Wang
中科院分区：
文献类型：
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作者：
He Lyu;Rongrong Wang
在信号量化中，众所周知，引入自适应量化方案可以提高它们在量化带限信号时的稳定性和准确性。然而，自适应量化只针对一维信号设计。本文的贡献有两个方面：(i)我们提出了第一类二维自适应量化方案，这些方案保持了与一维方案相同的数学和实际优点；（ii）我们表明，传统的一维和新的二维量化方案都可以有效地量化具有跳变不连续的信号，这使得在图像上使用自适应量化成为可能。在较温和的条件下，我们证明了利用自适应性，所提出的方法能够将图像的量化误差从目前最好的OP减小到更小的o，其中s是图像中的跳跃不连续点的数量，P （P比s）是样本总数。这种P/s倍的误差降低是通过应用全变分范数正则化解码器实现的，其公式的灵感来自压缩感知领域的数学超分辨率理论。与超分辨率设置相比，我们的误差降低是在不需要相邻尖峰/不连续被很好地分离的情况下实现的，这确保了其广泛的应用范围。
In signal quantization, it is well‐known that introducing adaptivity to quantization schemes can improve their stability and accuracy in quantizing bandlimited signals. However, adaptive quantization has only been designed for one‐dimensional signals. The contribution of this paper is two‐fold: (i) we propose the first family of two‐dimensional adaptive quantization schemes that maintain the same mathematical and practical merits as their one‐dimensional counterparts, and (ii) we show that both the traditional 1‐dimensional and the new 2‐dimensional quantization schemes can effectively quantize signals with jump discontinuities, which immediately enable the usage of adaptive quantization on images. Under mild conditions, we show that by using adaptivity, the proposed method is able to reduce the quantization error of images from the presently best OP to the much smaller Os , where s is the number of jump discontinuities in the image and P ( P≫s ) is the total number of samples. This P/s ‐fold error reduction is achieved via applying a total variation norm regularized decoder, whose formulation is inspired by the mathematical super‐resolution theory in the field of compressed sensing. Compared to the super‐resolution setting, our error reduction is achieved without requiring adjacent spikes/discontinuities to be well‐separated, which ensures its broad scope of application.