Systems and methods compress data and control data compression in borehole communication. The systems and methods convert original data collected by a sensor from a first domain into a second domain, wherein the original data is associated with one or more properties of an underground formation. A predetermined number of significant coefficients is selected from components of the second domain, wherein the predetermined number of significant coefficients are components of the second domain with largest amplitudes. The selected predetermined number of significant coefficients is quantized via an quantization technique and the selected predetermined number of significant coefficients is encoded into compressed data via an encoder.