Optimized Integer Cosine Transform

최적화 정수형 여현 변환

We present an optimized integer cosine transform(OICT) as an alternative approach to the conventional discrete cosine transform(DCT), and its fast computational algorithm. In the actual implementation of the OICT, we have used the techniques similar to those of the orthogonal integer transform(OIT). The normalization factors are approximated to single one while keeping the reconstruction error at the best tolerable level. By obtaining a single normalization factor, both forward and inverse transform are performed using only the integers. However, there are so many sets of integers that are selected in the above manner, the best OICT matrix obtained through value minimizing the Hibert-Schmidt norm and achieving fast computational algorithm. Using matrix decomposing, a fast algorithm for efficient computation of the order-8 OICT is developed, which is minimized to 20 integer multiplications. This enables us to implement a high performance 2-D DCT processor by replacing the floating point operations by the integer number operations. We have also run the simulation to test the performance of the order-8 OICT with the transform efficiency, maximum reducible bits, and mean square error for the Wiener filter. When the results are compared to those of the DCT and OIT, the OICT has out-performed them all. Furthermore, when the conventional DCT coefficients are reduced to 7-bit as those of the OICT, the resulting reconstructed images were critically impaired losing the orthogonal property of the original DCT. However, the 7-bit OICT maintains a zero mean square reconstruction error.