Multi-band wavelets have applied in many areas such as signal processing and numerical analysis due to their richer parameter space to have a more flexible time-frequency tiling, to give better energy compaction than 2-band wavelets. The sub-band operators are studied, an optimization model is built, and the wavelets with the smallest norm of the sub-band operator can be selected from the symmetric multi-band biorthogonal wavelets with free parameters, which can be applied in digital image processing based on wavelet theory and its fast algorithms. Firstly, the sub-band operator which is an infinite-dimensional matrix, is introduced, circular matrix theory is developed, and the norm of a sub-band operator associated to four-band wavelets with fast calculation structure is obtained. It is easy to obtain the norm of the sub-band operator with some structure by construction a function and computing the maximum. Secondly, a model to minimize the norm is built and four-band biorthogonal wavelets filter bands with fast calculation structure are designed. Lastly, an example is provided to illustrate the proposed results.