A signal processing method is provided. The method includes: generating an output signal containing a high-precision component at a level not determined by quantization of an input digital signal by subjecting each of pixels constituting the input digital signal to a predetermined filter operation such that a set of predetermined number of pixels including a target pixel and surrounding pixels thereof is obtained, the operation is carried out on the surrounding pixels when a variation from the target pixel is within a predetermined threshold range, and the operation is carried out on the target pixel when a variation from the target pixel is out of the predetermined threshold range; separating the high precision component from the signal output from the edge-preserving smoothing filter; and adding the high precision component separated from the high-precision component separating part to the input digital signal.