The QR decomposition with column pivoting (QRCP) is applied to a wavefront sensor based on the Talbot effect of two-dimensional grating, which significantly increases the number of subapertures, reduces the difficulty of sensor design, and accelerates wavefront reconstruction. After applying the QRCP method to the polynomial matrix, the number of rows of the polynomial matrix can be compressed to the same order as its columns. When reconstructing a higher-complexity and higher-order Zernike polynomial, the reconstruction speed of the solving process of Zernike coefficients increases to 224.00 times that of the traditional method, which makes it more suitable for calculations of adaptive optics. Additionally, this compression algorithm exhibits good robustness and can be applied to interferometers and Shack-Hartmann wavefront sensors. Its reduction ability creates a potential for simplifying and improving the sensor structure.