Informationpreserving

Information-preserving refers to properties or processes that retain information about the original data. In formal terms, a transformation is information-preserving if the original input can be recovered from the output without loss, given the defined domain.

From a mathematical or information-theoretic perspective, a deterministic mapping f: X → Y preserves information about X if f is injective on the support of X, and thus invertible on that support. In probabilistic terms, Y = f(X) preserves information about X when mutual information I(X; Y) equals H(X). When the mapping is not invertible, some information is irreversibly discarded.

Applications include lossless data compression, which aims to preserve all information for exact recovery; reversible data hiding; and invertible signal processing transforms, where the original signal can be reconstructed from transformed coefficients without loss. In cryptography, encryption preserves information in the sense that decryption recovers the plaintext, though the ciphertext is intended to conceal the information from unauthorized observers.

Limitations and caveats: in practice, information preservation is constrained by noise, finite precision, and deliberate information loss such as quantization, downsampling, or anonymization. The term is most meaningful when the process is defined to be invertible on the relevant domain, and when the notion of preserving information aligns with the possibility of exact or intended recovery of the original data.