A study on the optimal attributes of transform domain vector quantization for image and video compression

Abstract

It is well known that the optimal transform for scalar quantization is defined as the one that generates completely decorrelated transform coefficients. Under this definition, the Karhunen-Lo&ve transform is optimal and the discrete cosine transform is close to optimal. However, if vector quantization (VQ) is used in the transform domain, such a definition is no longer appropriate because compression performance of VQ is actually better when the components within the vector are more correlated. Therefore, the optimal transform for the purpose of VQ should reduce the correlation between the transform domain vectors and preserve the correlation among the components within each vector. In this paper, these two attributes are discussed, an intrinsic coupling factor is defined to quantitatively measure how closely the components are coupled within a vector, and a bitallocation mechanism is derived to assign bits to the transform domain vectors. Following the guidance of such a general study, a new scheme is proposed for image and video compression.

Study of High Dimensional Orthogonal Vector-Valued Wavelet with Scale 4

“…In real life, video images are vector-valued signals. Vector transforms have been recently studied for image coding by Li [5][6] , where input signals are finite vectors with same dimension and it has been shown that vector transforms have advantage in image coding at low bit rates. Another type of vector transforms has been discussed in [7].…”

Vector-valued wavelets and vector filter banks

“…Vector transforms have been recently introduced for image coding by , where input and output signals are nite vectors with same dimension. It was shown that vector transforms have advantage in image coding at low bit rates [3][4][5][6]. Moreover, vector quantization can be applied more easily in the vector transform domain than in the conventional scalar transform domain.…”

“…2 R. For more details, see[19][20][21][22]. In particular, if the interpolant in (4.1) is identical to the scaling function , the sampling formula(4In this case, we call that (t) is a scaling function with sampling property(or cardinal orthogonal scaling function (COSF), see 22]). It is clear 22] that a scaling function (t) is with sampling property if and only if (It was also shown in 24] that under certain regularity condition (4.4) is true if and only if h 0 = 0:5; h 2k = 0 for k 6 = 0; (4.5)where h k is the impulse response of the quadrature mirror lter H(!)…”