Linear gray enhancement is a spatial domain image enhancement technique commonly used in classical computers, mainly including image negative, image contrast stretching, and piecewise linear gray transformation. In order to realize these three linear gray enhancement techniques in the quantum computers, this paper proposes three types of linear gray transformation schemes for quantum images based on the generalized model of novel enhanced quantum image representation(GNEQR), and the quantum circuits that realize these three transformation methods are constructed according to the schemes. The proposed circuits take advantage of efficient quantum arithmetic operations and parallel Controlled-NOT modules to factor classical transformations into basic unitary operators such as the Controlled-NOT gates and the Toffoli gates. The results show that the linear gray enhancement algorithm for quantum images is better than the classical algorithm in both spatial complexity and time complexity.

Bilinear interpolation is widely used in classical signal and image processing. Quantum algorithms have been designed for efficiently realizing bilinear interpolation. However, these quantum algorithms have limitations in circuit width and garbage outputs, which block the quantum algorithms applied to noisy intermediate-scale quantum devices. In addition, the existing quantum bilinear interpolation algorithms can not keep the consistency between the geometric centers of the original and target images. To save the above questions, we propose quantum bilinear interpolation algorithms based on geometric centers using fault-tolerant implementations of quantum arithmetic operators. Proposed algorithms include the scaling-up and scaling-down for signals (grayscale images) and signals with three channels (color images). Simulation results demonstrate that the proposed bilinear interpolation algorithms obtain the same results as their classical counterparts with an exponential speedup. Performance analysis reveals that the proposed bilinear interpolation algorithms keep the consistency of geometric centers and significantly reduce circuit width and garbage outputs compared to the existing works.