Digital Image Interpolation in Matlab

6 Wavelet

In contrast to the Fourier analysis that decomposes the image into spectral components with infinite precision, wavelet transform represents the image by a set of analysis functions that are dilation and translations of a few functions with finite support. Conceptually, we can consider that the wavelet cuts up the image into different frequency components and studies each component with a resolution matched to its scale, also known as multi‐resolution analysis. The word “wavelet” that is used to describe such signal analysis and representation process as it captures the essence of the finite support (small kernel size) analysis functions has its root as “small wave” in Latin.

Unlike the blocked transform‐based image processing, the wavelet transform operates on the image as a whole but still has the same computational complexity. As a result, wavelet image processing is free from blocking artifacts as that observed in blocked transform (however, it will be shown in a sequel that blocking artifacts by other means can still be observed in wavelet‐based interpolated images). The forward dyadic wavelet transform (also known as analysis or decomposition) will decompose the signal into two components (and hence the word dyadic), known as the approximation and detail wavelet coefficients (which are also known as the subband signals). Such decomposition can be performed by the analysis multirate filter banks that are formed by subband filters followed by decimation ...