Storage systems often rely on multiple copies of the same compressed data, enabling recovery in case of binary data errors, of course, at the expense of a higher storage cost. In this paper, we show that a wiser method of duplication entails great potential benefits for data types tolerating approximate representations, like images and videos. We propose a method to produce a set of distinct compressed representations for a given signal, such that any subset of them allows reconstruction of the signal at a quality depending only on the number of compressed representations utilized. Essentially, we implement the holographic representation idea, where all the representations are equally important in refining the reconstruction. Here, we propose to exploit the shift sensitivity of common compression processes and generate holographic representations via compression of various shifts of the signal. Two implementations for the idea, based on standard compression methods, are presented: the first is a simple, optimization-free design. The second approach originates in a challenging rate-distortion optimization, mitigated by the alternating direction method of multipliers (ADMM), leading to a process of repeatedly applying standard compression techniques. Evaluation of the approach, in conjunction with the JPEG2000 image compression standard, shows the effectiveness of the optimization in providing compressed holographic representations that, by means of an elementary reconstruction process, enable impressive gains of several dBs in PSNR over exact duplications.

存储系统通常依赖于相同压缩数据的多个副本，从而在二进制数据错误的情况下进行恢复，当然会以更高的存储成本为代价。在本文中，我们显示了一种更明智的复制方法，对于容许近似表示（如图像和视频）的数据类型，它具有巨大的潜在优势。我们提出了一种为给定信号产生一组不同的压缩表示的方法，以使它们的任何子集都允许以仅取决于所利用的压缩表示的数量的质量来重构信号。从本质上讲，我们实现了全息表示的想法，其中所有表示对于完善重建都同样重要。这里，我们建议利用常见压缩过程的移位敏感性，并通过压缩信号的各种移位来生成全息表示。提出了基于标准压缩方法的两种实现方案：第一种是简单的，无需优化的设计。第二种方法源自具有挑战性的速率失真优化，通过乘数的交替方向方法（ADMM）缓解了这种失真，从而导致了重复应用标准压缩技术的过程。对该方法的评估与JPEG2000图像压缩标准一起，显示了优化在提供压缩全息表示方面的有效性，该全息表示通过基本重建过程实现了精确复制时PSNR令人印象深刻的几dB增益。第一个是简单，无需优化的设计。第二种方法源自具有挑战性的速率失真优化，通过乘数的交替方向方法（ADMM）缓解了这种失真，从而导致了重复应用标准压缩技术的过程。对该方法的评估与JPEG2000图像压缩标准一起，显示了优化在提供压缩全息表示方面的有效性，该全息表示通过基本重建过程实现了精确复制时PSNR令人印象深刻的几dB增益。第一个是简单，无需优化的设计。第二种方法源自具有挑战性的速率失真优化，通过乘数的交替方向方法（ADMM）缓解了这种失真，从而导致了重复应用标准压缩技术的过程。对该方法的评估与JPEG2000图像压缩标准一起，显示了优化在提供压缩全息表示方面的有效性，该全息表示通过基本重建过程实现了精确复制时PSNR令人印象深刻的几dB增益。