Construction For A Kind Of Three-channel Tight Frame

With the development of wavelet, people find that haar wavelet is the only compactly-supported,symmetric and orthogonal wavelet. Then people give up orthogonality to design wavelet frames. Tight wavelet frames with the condition A=B=1 do not produce redundant, so people begin to design such tight wavelet frame and has got some results in theory and application. In the [1], Chui and He proved that the inequality (the Sub-QMF condition)is the sufficient condition of existence of three-channel tight frame. In recent years, we begin to pay attention to the design of tight frame filter with parameters. From the low-pass filter to construct the tight frame, we can elect low-pass filter of better nature. In the article[10] WANG Hai-hui gave a series of four-channel tight frame filters by this method. In the[10], we get the low-pass filter form whose corresponding scaling function satisfies the Sub-QMF condition.On these basic, we give the formula with the parameter r of three-channel tight frame in the use of Householder matrix filter design methods mentioned in[1] which is applied to a group of length of 4 low-pass filter with the parameter r and better nature. The low-pass filter is:The parameter r satisfies the inequality 0≤r <(?). When the parameters take different values, we get two high-pass filters for the length of 4. The two high-pass filters are:and We elect a tight frame (r=0.2)with better smoothness and symmetry properties. This frame is applied in image fusion experiment. Through our observation and data analysis we conclude that the research about three-channel tight frame is necessary.