  We consider the case when a set of spatially distributed sensors make local
observations which are noisy versions of a signal of interest. Each sensor
transmits compressed information about its measurements to the fusion center
which should recover the original signal within a prescribed accuracy. Such an
information processing relates to a wireless sensor network (WSN) scenario.
  The key problem is to find models of the sensors and fusion center so that
they will be optimal in the sense of minimization of the associated error under
a certain criterion, such as the mean square error (MSE). We determine the
models from the technique which is a combination of the maximum block
improvement (MBI) method and the generic Karhunen-Lo\`{e}ve transform (KLT).
The resulting multi-compressor KLT-MBI algorithm is given in terms of
pseudo-inverse matrices and, therefore, it is numerically stable and always
exists. The proposed model provides compression, de-noising and reconstruction
of distributed signals for the cases when known methods either are not
applicable (because of singularity of associated matrices) or produce larger
associated errors. Error analysis is provided.
