On the regular structure for the fast 2-D DCT algorithm

Direct Recursive Structures for Computing Radix-<tex>$r$</tex>Two-Dimensional DCT/IDCT/DST/IDST

“…Considering other fast algorithms in [7] and [14], the DCT which maps the 2-D index of input sequence to the new 1-D index is decomposed into length-1-D DCTs. By employing other fast 1-D DCT algorithms, such as Hou's [6], the 2-D DCT is computed more effectively.…”

“…To reduce their computational complexities and facilitate real-time implementation, the development of fast and efficient algorithms for computing 2-D DCT/IDCT becomes increasingly important. Several fast algorithms for 2-D DCT were proposed to reduce the computational complexity [6]- [14]. More efficient algorithms compute directly on the 2-D data by fully exploiting the 2-D characteristic of kernel functions [15]- [19].…”

On the fixed-point error analysis of several fast IDCT algorithms

“…As shown in Fig. 5, the Cho-Lee algorithm is composed of three stages [5], [6]. The first stage performs successive additions and subtractions; the second stage computes N 1-D IDCT's; and the third stage also performs only addition and subtraction.…”

“…Thus, the first stage can be removed from the analysis, making the second stage the only error source. As described in [5] and [6], the third stage consists of butterflies as shown in Fig. 6.…”

“…However, for more efficient computation, many fast algorithms [5]- [9] that work directly on the 2-D data set have recently been proposed. Among these, the most efficient 2-D DCTADCT algorithms is the Cho and Lee algorithm [5], [6]. In [5], it is shown that only N 1-D IDCT's are required for the computation of N x N IDCT.…”