A fractional overcomplete wavelet transform’s filter banks, which are half symmetrical, approximately shift-invariant and minimumeven-length
is designed and constructed. A novel designing scheme for the symmetrical and minimum-even-length low-pass filter
bank is proposed. High-pass filter banks with approximately shift-invariant property are constructed through Toeplitz matrix
factorization, which is easier than the existing methods. This type of wavelet is expected to provide favourable conditions to image
denoising. Fractional overcomplete wavelet transform gives better denoising than existing wavelets including orthogonal compact
support dyadic wavelet and orthogonal symmetrical M-band wavelet system.