1. An image processing apparatus that removes noise from an input image, the image processing apparatus comprising: an edge-preserved smoothing processing unit that creates a basic-structure component image representing an image that the input image except edge is smoothed while preserving the edge in the input image; a difference processing unit that creates a detail component image representing an image that the basic-structure component image created by the edge-preserved smoothing processing unit is subtracted from the input image; a multiresolution transform processing unit that performs multiresolution transform processing of decomposing the detail component image created by the difference processing unit into a plurality of frequency-band images; a noise removing processing unit that performs noise removal on the frequency-band images created by the multiresolution transform processing unit; and an inverse multiresolution transform processing unit that performs inverse multiresolution transform processing of combining the frequency-band images from which noises are removed by the noise removing processing unit, thereby creating a noise-removed detail-component image.