公开(公告)号：CA2094524A1

公开(公告)日：1994-01-31

申请号：CA2094524

申请日：1993-04-21

Applicant: IBM

Inventor： FEIG EPHRAIM ,  LINZER ELLIOT N

IPC: H03M7/30 ,  G06F17/14 ,  G06T9/00 ,  G06T11/60 ,  H04N7/26 ,  H04N7/30 ,  H04N11/04 ,  H04N7/12 ,  G06F5/00 ,  G06T1/00 ,  G06F3/14

Abstract: YO992-037 This invention minimizes the number of non-trivial multiplications in the DCT process by rearranging the DCT process such that non-trivial multiplications are combined in a single process step. In particular, the DCT equations for the row-column application of the DCT process on k=pq points wherein p and q are relatively prime, are factored into permutation matrix, a tensor product between matrices having pxp and qxq points, and a matrix whose product with an arbitrary vector having pq points requires pq - p - q + 1 additions and/or subtractions. The tensor product is then further factored to remove non-trivial multiplications by developing a a first factor having (pq - p - q + 1)/2 non-trivial multiplications and a diagonal matrix. The diagonal matrix is not unique or any set of data. Its jj-th elements are chosen from a subproduct of the factorization of the tensor product. Once the diagonal matrix elements are chosen the remaining first factor is developed. When the factorization is complete, the diagonal matrix is absorbed into the quantization step which follows the DCT process. The quantization step is the multiplication of a diagonal matrix by the DCT output data. The quantization diagonal matrix is combined with the diagonal matrix of the DCT to form one multiplication process by which nontrivial element multiply data. This combination of multiplication steps reduces the number on non-trivial multiplications in the DCT process. In addition, the same factorization technique is applicable to the two dimensional direct application of the DCT to an kxk matrix of points. Specifically, the transform matrix on kxk points is defined to be the tensor product of the transform matrix on k points with the transform matrix on k points. This results in the individual factors of the transform matrix on k points forming a tensor product with themselves and demonstrates that the factorization on k points also reduces the number o non-trivial multiplications on the transform matrix on kxk points. In addition, and similarly, the same factorization technique is applicable to to the application of the inverse DCT on k points and to the inverse two dimensional DCT on a k x k matrix of points. Specifically, the inverse transforms are obtained by transposition of the factorization of the forward transforms, because the DCT is an orthogonal operator and hence its inverse equals its transpose. Alternately, the inverse transforms are obtained by direct inversion of the individual factors in the factorization of the forward transform.