1. A method to improve characterization of a surrounding formation comprising: obtaining input multidimensional sonic measurements from receivers of a sonic measurement tool after having activated a transmitter; processing the input multidimensional sonic measurements via a quantizer according to a bit reduction parameter to generate processed input multidimensional sonic measurements, wherein the quantizer comprises a quantizer bit shift adjuster that causes quantization to not be performed if an incoming data block is weak; decorrelating, with a processor, the processed input multidimensional sonic measurements to determine decorrelated multidimensional sonic measurements, the input multidimensional sonic measurements having a plurality of dimensions corresponding to a respective plurality of azimuthal directions from which the input multidimensional sonic measurements were measured by sonic tools, the decorrelated multidimensional sonic measurements being decorrelated among the plurality of dimensions of the input multidimensional sonic measurements; processing, with the processor, the decorrelated multidimensional sonic measurements to determine compressed data representative of the input multidimensional sonic measurements; and transmitting the compressed data to a surface system via a telemetry link in order to characterize the surrounding formation.