Quantum Discrete Cosine Transform for Image Compression

Chao-Yang Pang, Ri‐Gui Zhou, Ben-Qiong Hu +2 more

Yan Ma, Nanrun Zhou

Pang, Chao Yang, Zheng Zhou, Guo, Guang Can

Discrete Cosine Transform (DCT) is very important in image compression. Classical 1-D DCT and 2-D DCT has time complexity O(NlogN) and O(N²logN) respectively. This paper presents a quantum DCT iteration, and constructs a quantum 1-D and 2-D DCT algorithm for image compression by using the iteration. The presented 1-D and 2-D DCT has time complexity O(sqrt(N)) and O(N) respectively. In addition, the method presented in this paper generalizes the famous Grover's algorithm to solve complex unstructured search problem.

Felix Montalfu, Seham Al Abdul Wahid, Farah Mohammadi +1 more

The Discrete Cosine Transform (DCT) is an integral part of classical image compression, which becomes the basis of the JPEG standard. With advances in quantum computing, there is growing interest in exploring quantum analogues of classical algorithms for such transforms. This paper presents a simulation of the Quantum Discrete Cosine Transform (QDCT) using the Qiskit Python library, applied to standard grayscale images segmented into 8x8 and 4x4 blocks. The QDCT algorithm is formulated as a unitary operator and evaluated using state-vector simulation. Due to the current constraints of quantum hardware and challenges in circuit synthesis, this study focused on simulation results, as direct quantum circuit measurement leads to amplitude collapse and unusable output. The performance of QDCT is quantitative compared to classical DCT using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and compression ratio metrics. The result of this study reveals the feasibility and current limitations of QDCT-based image compression while providing a reproducible benchmark for future quantum image processing research. This study offers a realistic assessment of the potential and technical limitations of QDCT in the context of emerging quantum technologies.

Д.Т. Мухамедиева, Р.А. Собиров, N. M. Turgunova +1 more

Shiwen An, Zhongyi Ni, Huanhai Zhou +1 more

The Discrete Fourier Transform (DFT), the Discrete Cosine Transform (DCT), and their block-wise variants underpin most deployed image and video codecs. Their effectiveness rests on three properties: their runtime is near-linear (up to a polylogarithmic factor) in the image size, they are exactly invertible, and they carry few to no parameters. We generalize these transforms to dataset-adaptive isometric multilinear bases that keep all three properties at the cost of a polylogarithmic number of parameters, by parameterizing each basis as an isometric tensor network, inspired by quantum many-body theory, and training one shared basis per image dataset with Riemannian optimization. Because the family contains the DFT and the DCT-IV (a variant of the DCT) as exact points, training can start from these transforms, and it improves on its starting point at the compression level it is trained for. We evaluate the bases on natural photographs and line drawings. On photographs, which the cosine basis already fits well, the best trained basis leads the DCT only under aggressive truncation. On Quick Draw line drawings, under a common codec at matched quality, the best trained basis stores each image in about 20% fewer bytes than the 8x8 block cosine transform of the Joint Photographic Experts Group (JPEG) format, not counting the one-off storage of the basis.