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The double-density discrete wavelet transform(DWT) is an improvement upon the critically sampled DWT with important additional properties. It employs one scaling function and two distinct wavelets, which are designed to be offset from one another by one half. And it is overcomplete by a factor of two. Also, this transformation is nearly shift-invariant. But there is room for improvement because not all of the wavelets are directional. That is, although the double-density DWT utilizes more wavelets, some lack a dominant spatial orientation, which prevents them from being able to isolate those directions. Proposed method is a DWT that combines the double-density DWT and quincunx sampling, each of which has its own characteristics and advantages. Especially, the quincunx sampling treats the different directions more homogeneously. As a result, since proposed method can generate sub-images of multiple degrees rotated versions, this method provides an improved performance in image processing fields.

The general wavelet transform has profitable property in non-stationary signal analysis specially. The tunable Q-factor wavelet transform is a fully-discrete wavelet transform for which the Q-factor Q and the asymptotic redundancy r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented. The transform is based on a real valued scaling factor and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. The transform is parameterized by its Q-factor and its over-sampling rate, with modest over-sampling rates being sufficient for the analysis/synthesis functions to be well localized. This paper describes filter design of 2D discrete-time wavelet transform for which the Q-factor is easily specified. With the advantage of this transform, perfect reconstruction filter design and implementation for performance improvement are focused in this paper. Hence, the 2D transform can be tuned according to the oscillatory behavior of the image signal to which it is applied. Therefore, application for performance improvement in multimedia communication field was evaluated.

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