  This paper mainly focuses on the problem of lossy compression storage from
the perspective of message importance when the reconstructed data pursues the
least distortion within limited total storage size. For this purpose, we
transform this problem to an optimization by means of the importance-weighted
reconstruction error in data reconstruction. Based on it, this paper puts
forward an optimal allocation strategy in the storage of digital data by a kind
of restrictive water-filling. That is, it is a high efficient adaptive
compression strategy since it can make rational use of all the storage space.
It also characterizes the trade-off between the relative weighted
reconstruction error and the available storage size. Furthermore, this paper
also presents that both the users' preferences and the special characteristic
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, the data
with uniform information distribution is incompressible, which is consistent
with that in information theory.
