Enhancing image representation and compression: An innovative Nz-Nqer framework with block truncation quantum coding

Efficiently representing and compressing large-scale images in quantum circuits remains a challenge due to increasing circuit complexity. This paper proposes an innovative approach called NZ-NEQR (Non-Zero Novel Quantum Representation) to tackle this issue. Eliminating zero connections from the existing NEQR approach significantly reduces the complexity of state label preparation. The proposed NZ-NEQR approach achieves remarkable improvements in both image representation and compression, leading to a substantial reduction in required bits per pixel. To further enhance compression, Block Truncation Coding (BTC) is adopted as a compression scheme, which effectively truncates images into two labels suitable for quantum compression and reconstruction. Notably, the proposed method requires fewer bits per pixel compared to existing NEQR approaches. Additionally, NZ-NEQR combined with BTC employs only 5 qubits for representing a $1024 \times 1024$ image, and compression using a $4 \times 4$ quantum BTC block represents a significant advancement. Computational results demonstrate the superior effectiveness of the proposed NZ-NEQR approach combined with BTC for quantum image representation and compression, surpassing the performance of NEQR and JPEG approaches.