  We study the problem of multi-compression and reconstructing a stochastic
signal observed by several independent sensors (or compressors) that transmit
compressed information to a fusion center. { The key aspect of this problem is
to find models of the sensors and fusion center that are optimized in the sense
of an error minimization under a certain criterion, such as the mean square
error (MSE).} { A novel technique to solve this problem is developed. The
novelty is as follows. First, the multi-compressors are non-linear and modeled
using second degree polynomials. This may increase the accuracy of the signal
estimation through the optimization in a higher dimensional parameter space
compared to the linear case. Second, the required models are determined by a
method based on a combination of the second degree transform (SDT) with the
maximum block improvement (MBI) method and the generalized rank-constrained
matrix approximation. It allows us to use the advantages of known methods to
further increase the estimation accuracy of the source signal. Third, the
proposed method is justified in terms of pseudo-inverse matrices. As a result,
the models of compressors and fusion center always exist and are numerically
stable.} In other words, the proposed models may provide compression,
de-noising and reconstruction of distributed signals in cases when known
methods either are not applicable or may produce larger associated errors.
