Multi-resolution Analysis Using Symmetrized Odd and Even DCT Transforms

Multi-resolution signal analysis proved to be very effective tool for many applications that widely serve both research as well as professional communities. The wavelet transform is one of the most popular techniques for multi-resolution analysis of signals, however, the complexity of the wavelet transform combined with difficulty in selecting a unique wavelet that maintains the same performance for several applications makes our proposed DCT symmetrization technique very attractive particularly for its uniqueness and simplicity. In this regard, a novel procedure for multi resolution analysis through combining two independent discrete cosine transforms derived from the traditional DCT, the even discrete cosine transform and the odd discrete cosine transform. The even transform is used to compute the even DCT coefficients while the odd transform is used to compute odd coefficients. The separation of the traditional DCT into two independent transforms combined with a discrete sample symmetrization procedure, allows dyadic signal analysis and multi-resolution reconstruction using even, odd or a combination of both transforms. Our preliminary results indicated that the odd inverse discrete cosine transform can be used to compute the error of reconstruction while a combination of the two transforms can be used to analyze signals in dyadic multi resolution structure. Experimental results are presented to demonstrate the effectiveness of the proposed multi resolution approach to analyze signals and combine filtering/denoising in one operation.