The wavelet decomposition Wavelets have been widely used in many image processing applications including compression, enhancement, reconstruction, and image analysis, and a wavelet transformation provides a multiscale decomposition of the image data. Notice that the number of transform coefficients is exactly the same as the number of pixels in the original image. Fast algorithms exist for computing the forward and inverse wavelet transforms. Desired intermediate levels can be easily reconstructed as illustrated in Figure 2. Coarse resolution data are accessed more frequently than the higher resolution information, and hence can be stored in faster devices for efficient browsing.
Image compression is also important in storing large amount of data.
Many GIS and medical imaging applications often require lossless compression. Although the total number of wavelet coefficients equals the number of pixels in the images, their storage requirements differ. The original intensity data, in most cases, consists of only integer numbers. Wavelet coefficients, in general, are real numbers, thus requiring more memory. Even for the case of no compression, these coefficients need to be quantized and encoded appropriately to ensure that they do not take more space than the original image data.