Integer discrete cosine transform via lossless Walsh-Hadamard transform with structural regularity for low-bit-word-length

This paper presents an integer discrete cosine transform (IntDCT) with only dyadic values such as k/2ⁿ (k, n ∈ ℕ). Although some conventional IntDCTs have been proposed, they are not suitable for lossless-to-lossy image coding in low-bit-word-length (coefficients) due to the degradation of the frequency decomposition performance in the system. First, the proposed M-channel lossless Walsh-Hadamard transform (LWHT) can be constructed by only (log₂ M)-bit-word-length and has structural regularity. Then, our 8-channel IntDCT via LWHT keeps good coding performance even if low-bit-word-length is used because LWHT, which is main part of IntDCT, can be implemented by only 3-bit-wordlength. Finally, the validity of our method is proved by showing the results of lossless-to-lossy image coding in low-bit-word-length.