The invention relates to an 
observation matrix construction method based on a low-coherence unit norm 
tight frame, and belongs to the technical field of 
signal processing, and the method comprises thesteps: S1, initializing an initial 
observation matrix phi 0 into a random part Fourier matrix, and enabling the initial 
observation matrix phi 0 to serve as an initial alpha 
tight frame F; s2, calculating a 
Gram matrix corresponding to the framework F, and projecting the matrix to a structure constraint set of a tight framework by using a 
contraction function to generate a new 
Gram matrix; s3, updating the 
Gram matrix through a weighted 
iteration process; s4, reducing the rank of the new Gram matrix, calculating the square root of the new Gram matrix, and finding out a 
tight frame closest toa unit norm tight frame; and S5, solving the optimal target function to obtain an observation matrix. According to the method, the mutual interference coefficient between the observation matrix and the sparse basis is reduced, the dependence degree on 
signal sparsity is reduced, the problem that an ETF frame is difficult to construct is avoided, the initial observation matrix is initialized into apart of Fourier matrix, the calculation complexity is reduced, and the pressure of storage and 
processing equipment is reduced.