1. An image processing device comprising: a first frequency separator, implemented by at least one hardware component, which receives an input image and performs frequency separation on the input image into a first low-frequency component and a first high-frequency component that includes a higher-frequency component than the first low-frequency component; a second frequency separator, implemented by at least one hardware component, which separates the first low-frequency component into a second low-frequency component and a second high-frequency component that includes a higher-frequency component than the second low-frequency component; a first image transformer, implemented by at least one hardware component, which performs noise removal on the second low-frequency component and on the second high-frequency component, and outputs a noise-removed image as a first transformed image; and a second image transformer, implemented by at least one hardware component, which performs noise removal on the first high-frequency component and on the first transformed image, with fewer resources allocated than those allocated to the first image transformer, and outputs a noise-removed image as a second transformed image; wherein the first frequency separator comprises a first wavelet transformer which performs a wavelet transform, and wherein the second frequency separator comprises a second wavelet transformer which performs a wavelet transform, and wherein the first image transformer comprises: a first wavelet shrinker, implemented by at least one hardware component, which compares a wavelet coefficient for the second high-frequency component with a first threshold value, and shrinks any wavelet coefficient that is smaller than the first threshold value; and a first inverse wavelet transformer, implemented by at least one hardware component, which reconstructs an image by performing an inverse wavelet transform on a signal that is output from the first wavelet shrinker and on the second low-frequency component, and wherein the second image transformer comprises: a second wavelet shrinker, implemented by at least one hardware component, which compares a wavelet coefficient for the first high-frequency component with a second threshold value, and shrinks any wavelet coefficient that is smaller than the second threshold value; and a second inverse wavelet transformer, implemented by at least one hardware component, which reconstructs an image by performing an inverse wavelet transform on a signal that is output from the second wavelet shrinker and on the first transformed image.