Wavelet transforms on two-dimensional images

This paper studies the two-dimensional wavelet transform applied to two-dimensional images. The classical technique oftentimes implements the Fourier transform. This paper offers a brief discussion regarding the comparison of the two transforms on a single alphabet. It provides a comparison of the global properties present in the Fourier transform technique versus a more localized analysis when the wavelet transform is applied to the same image. The wavelet selected in this study is the derivative of the Gaussian since in some sense offers a nice comparison to the Fourier method.