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This study concentrates on fuzzy relational calculus regarded as a basis of data compression. In this setting, images are represented as fuzzy relations. We investigate fuzzy relational equations as a basis of image compression. It is shown that both compression and decompression (reconstruction) phases are closely linked with the way in which fuzzy relational equations are being usually set and solved. The theoretical findings encountered in the theory of these equations are easily accommodated as a backbone of the relational compression. The character of the solutions to the equations make them ideal for reconstruction purposes as they specify the extremal elements of the solution set and in such a way help establish some envelopes of the original images under compression. The flexibility of the conceptual and algorithmic framework arising there is also discussed. Numerical examples provide a suitable illustrative material emphasizing the main features of the compression mechanisms