In the Hadamard transform imaging spectrometer, the Hadamard decoding is very important, and the noise brings an affect on the decoding to a certain extent. The basic principles of the Hadamard transform imaging spectrometer are described. On this basis, the inverse filtering method for Hadamard decoding algorithms is analyzed. In the actual imaging process, the noise will be inevitably introduced. Through analysis, the impact of the Gaussian blur noise on the Hadamard decoding algorithm is primarily studied, the computer simulation results are given. It is very important for the further study of Hadamard decoding algorithm.