Fast Binary Wavelet Transform

고속 이진 웨이블렛 변환

A theory of binary wavelets has been recently proposed by using two-band perfect reconstruction filter banks over binary field . Binary wavelet transform (BWT) of binary images can be used as an alternative to the real-valued wavelet transform of binary images in image processing applications such as compression, edge detection, and recognition. The BWT, however, requires large amount of computations since its operation is accomplished by matrix multiplication. In this paper, a fast BWT algorithm which utilizes filtering operation instead or matrix multiplication is presented . It is shown that the proposed algorithm can significantly reduce the computational complexity of the BWT. For the decomposition and reconstruction or an N ${\times}$ N image, the proposed algorithm requires only 2LN$^2$ multiplications and 2(L-1)N$^2$addtions when the filter length is L, while the BWT needs 2N$^3$multiplications and 2N(N-1)$^2$additions.