The invention discloses a self-adaptive reconstruction and an uncompressing method for 
power quality data based on a compressive sensing theory. A 
power quality data compression process with concurrent sampling and compression is achieved through a random measurement matrix, compressive sensing thoughts are used to perform sparse 
decomposition on the 
power quality data, sparse signals are subjected to 
Gaussian measurement encoding, and a self-
adaptive matching pursuit 
algorithm is applied to reconstruct signals. According to the self-adaptive reconstruction and the uncompressing method, the random measurement matrix is simple in structure and quick in operation, in no need of 
intermediate variable storage space and independent of power disturbance 
signal characteristics, and has universality; compared with greedy algorithms of an orthogonal 
matching pursuit and the like, known sparseness is not needed, self adaption and regularization processes are provided, the 
operation time is short, and accurate reconstruction can be achieved; and constraints of compression after sampling of traditional 
data compression methods are broken through, little sampling can recover original power quality signals well, and accordingly, requirements for hardware can be reduced, and the compression efficiency is improved.