The degradation of imaging quality caused by environmental noise during Fourier single pixel imaging (FSPI) is a big problem. In this paper, we propose simple and efficient denoised single-pixel imaging schemes by using linear filters to reduce the impact. Two filters, such as an average filter and Gaussian filter, are employed, and their corresponding schemes are named SCH-A and SCH-G, respectively. The experimental and simulation results show that both schemes can effectively reduce the impact of environmental noise and have greater robustness in comparison with those using the deringing SPI and conventional SPI. Compared with SCH-A, the reconstructed image by SCH-G keeps more details and edges. With the increase of template size, SCH-A and SCH-G have better filtering effects with the same variance. Meanwhile, the larger the template size is, the better filtering effect SCH-A has. This conclusion is also applicable to SCH-G under the same variance.