Biorthogonal balanced multiwavelets with high armlets order and their application in image denoising

Multiple approaches can be used to meet the nth order wavelet analysis consistency requirement between balanced multiwavelets and armlets. Due to the complexity of the n-balancing conditions, it is difficult to construct a family of n-balanced orthogonal multiwavelets for a relatively large n. In this paper, we introduce a convenient way to construct symmetric/antisymmetric biorthogonal multiwavelets provided that both the balanced order n≥2 and the high armlets order conditions are met. First, we introduce the concept of biorthogonal armlets and illustrate a relationship among the four filter banks of a biorthogonal system. Then we present an algorithm for constructing biorthogonal balanced multiwavelets with armlets order (BBMA) and compute a novel class of such multiwavelets. Finally, we investigate the performances of BBMA and existing wavelets on the application of image denoising. Simulation results show that BBMA typically result in improved denoising.