  A novel approach is presented to unfold particle hit positions in tracking
detectors with multiplexed readout representing an underdetermined system of
linear equations. The method does not use any prior information about the hit
positions, the only assumption in the procedure is that isolated hit signals
generated on consecutive detector strips follow a smooth distribution.
Ambiguities introduced by charge sharing from multiplexing are reduced by using
a regularization technique. We have tested this method on a multiplexed 50x50
cm$^{2}$ Micromegas detector with 1037 strips and only 61 readout channels,
using cosmic rays, and we have found that single and multiple clusters of hits
can be reconstructed with high efficiency.
