Fig. 1. A 2 × 2 color image and its NCQI representation

Fig. 2. Quantum circuit of $C{S}_{X+}$

Fig. 3. Quantum circuit of $N$-bit adder

Fig. 4. (a) CGC, (b) ICGC and (c) simplified quantum circuit of $N$-bit comparator

Fig. 5. Design flow of the quantum circuit for filtering

Fig. 6. Quantum circuit preparation of color image

Fig. 7. Quantum circuit preparation for neighborhood pixels

Fig. 8. Quantum circuit of difference computing module (MDC)

Fig. 9. Quantum circuit of vector distance calculation module

Fig. 10. Quantum circuit of neighborhood aggregation distance calculation module

Fig. 11. Quantum circuit of vector median extraction

Fig. 12. Quantum circuit of median pixel replacement

Fig. 13. Quantum circuit of quantum image vector median filter

Fig. 14. (a) Strawberries; (b) Flowers; (c) Lenna; (d) Peppers; (e) Baboon

Fig. 15. (a)-(e) are noised images and denoise images of five experimental images respectively, where the Noised column is the noised image, and the QBMF, VMF and QVMF columns are the images processed by quantum Boolean mean filtering, proposed scheme and classical vector median filtering respectively