Recently, substantial efforts have been made to find an alternative approach to the Shannon sampling theorem with a method that can deal with large data sets, something for which the Shannon theorem is not easily applicable. If applied, the above approach would have to surmount difficult computational problems resulting from large data. In order to deal with the large data sets, we avoid a universal image acquisition and use wavelet matrices based on tree structures. The proposed approach allows a calculation reduction that yields a better control over the compressed image quality. The suggested technique also advocates a selective approach over the non-adaptive, random functions favored by the Shannon sampling theorem.