This paper mainly focuses on the problem of lossy compression storage based on the data value that represents the subjective assessment of users when the storage size is still not enough after the conventional lossless data compression. To this end, we transform this problem to an optimization, which pursues the least importance-weighted reconstruction error in data reconstruction within limited total storage size, where the importance is adopted to characterize the data value from the viewpoint of users. Based on it, this paper puts forward an optimal allocation strategy in the storage of digital data by the exponential distortion measurement, which can make rational use of all the storage space. In fact, the theoretical results show that it is a kind of restrictive water-filling. It also characterizes the trade-off between the relative weighted reconstruction error and the available storage size. Consequently, if a relatively small part of total data value is allowed to lose, this strategy will improve the performance of data compression. Furthermore, this paper also presents that both the users’ preferences and the special characteristics of data distribution can trigger the small-probability event scenarios where only a fraction of data can cover the vast majority of users’ interests. Whether it is for one of the reasons above, the data with highly clustered message importance is beneficial to compression storage. In contrast, from the perspective of optimal storage space allocation based on data value, the data with a uniform information distribution is incompressible, which is consistent with that in the information theory.

中文翻译：

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具有消息重要性的数字数据的存储空间分配策略

本文主要针对在常规无损数据压缩后存储容量仍然不够的情况下，基于代表用户主观评价的数据值的有损压缩存储问题。为此，我们将这个问题转化为优化，在有限的总存储空间内，追求数据重构中的最小重要性加权重构误差，其中从用户的角度采用重要性来表征数据值。在此基础上，本文提出了一种基于指数失真度量的数字数据存储优化分配策略，可以合理利用所有存储空间。事实上，理论结果表明它是一种限制性注水。它还表征了相对加权重建误差和可用存储大小之间的权衡。因此，如果允许总数据值中相对较小的一部分丢失，则该策略将提高数据压缩的性能。此外，本文还提出，用户的偏好和数据分布的特殊性都可以触发小概率事件场景，即只有一小部分数据可以覆盖绝大多数用户的兴趣。无论是出于上述原因之一，具有高度聚集消息重要性的数据有利于压缩存储。相比之下，从基于数据值的最优存储空间分配的角度来看，信息分布均匀的数据是不可压缩的，