Noise-robust computational ghost imaging with pink noise speckle patterns

We propose a computational ghost imaging (CGI) scheme using customized pink noise speckle pattern illumination. By modulating the power spectrum distribution of the speckles, we generate speckle patterns with a significant positive spatial intensity fluctuation correlation. We experimentally reconstruct images using our synthesized speckle patterns in the presence of a variety of noise sources and pattern distortion and show it is robust to noise environment. The results are compared with the use of standard white noise speckle patterns. We show that our method gives much better image qualities under different types of noise than the traditional way. The proposed scheme promises potential applications in underwater, dynamic, and moving target CGI.

Figure 1

(a), (b), and (c): The 1D PSD, a typical speckle pattern, and spatial intensity fluctuation correlation of customized pink noise patterns. (d), (e), and (f): The 1D PSD, a typical speckle pattern, and spatial intensity fluctuation correlation of standard white noise patterns. Compared with white noise, there is a strong positive cross-correlation between a pink noise pixel and its neighbors.

Figure 2

Comparison of the intensity distribution for white and pink noise speckle patterns. A $10\times 10$ pixel area was chosen on the pattern and summed up as the intensity for one-time sampling; 200 patterns are used to achieve intensity sequency that gives the intensity distribution corresponding to the sequence of patterns. The pink noise speckle (dash-dotted red line) has a much larger fluctuation as compared with the white noise speckle (solid black line), while their average intensities (“$+$” dotted blue line, and dashed green line) are the same.

Figure 3

(a) Schematic of the basic setup for a CGI experiment without noise. A CW laser is reflected by the DMD where the noise patterns are loaded. The reflected laser imprinted with noise patterns is imaged onto the object surface with the letters TH. A CCD put right after the object is used as a bucket detector in all the experiments in this work. The dashed frame is the part we modify by introducing a variety of noise sources. (b)–(d) CGI with white noise speckle illumination using 800, 1500, and 5292 patterns; (c)–(f) CGI with pink noise speckle illumination using 800, 1500, and 5292 patterns; (h) MSE distribution with sampling numbers of 500, 800, 1500, 3000, 4500, and 5292. The dashed blue line and solid red line correspond to the evaluation of CGI results reconstructed by white and pink noise patterns, respectively.

Figure 4

(a) Schematic of the setup with environmental noise introduced by a light bulb put in front of the object; (b)–(d) CGI with white noise speckle illumination using 800, 1500, and 5292 patterns, respectively; (c)–(f) CGI with pink noise speckle illumination using 800, 1500, and 5292 patterns, respectively. CGI with white noise is blurred until distinguishable from background noise at full sampling (5292) due to the strong background noise, while the CGI with pink noise retrieves the image at low sampling rate; (h) MSE distribution with sampling number at 500, 800, 1500, 3000, 4500, and 5292. The dashed blue line and solid red line correspond to evaluation on CGI results reconstructed by white and pink noise patterns. It shows that the MSE of pink noise at 500 sampling number is already better than the white noise at full sampling number (5292).

Figure 5

(a) Schematic of the setup. A ground glass diffuser (grit size 220) is put in front of the object to diffuse the speckle patterns, and a light bulb is also put in front of the object to introduce further environment noise; (b)–(d) CGI with white noise speckle illumination using 800, 1500, and 5292 patterns; (c)-(f) CGI with pink noise speckle illumination using 800, 1500, and 5292 patterns. CGI with white noise is blurred and indistinguishable even at full sampling (5292) due to the strong background noise and diffraction, while the CGI with pink noise shows the image; (h) MSE distribution with sampling numbers of 500, 800, 1500, 3000, 4500, and 5292. The dashed blue line and solid red line correspond to the evaluation of CGI results reconstructed by white and pink noise patterns, respectively.

Figure 6

(a) Schematic of the setup with an iris inserted right after the lens. The diameter of the iris is 1000 $\mu \mathrm{m}$. The speckle patterns are diffracted due to the iris; (b)–(d) CGI with white noise speckle illumination using 800, 1500, and 5292 patterns; (c)–(f) CGI with pink noise speckle illumination using 800, 1500, and 5292 patterns. CGI with white noise is blurred and indistinguishable at 800 and 1500 sampling number and has low contrast to background at 5292. However, the CGI with pink noise retrieves clear images; (h) MSE distribution with sampling numbers of 500, 800, 1500, 3000, 4500, and 5292. The dashed blue line and solid red line correspond to the evaluation of CGI results reconstructed by white and pink noise patterns, respectively.

Figure 7

(a) Schematic of the setup with environmental noise introduced by a light bulb put in front of the detector; (b)-(d) CGI with white noise speckle illumination using 800, 1500, and 5292 patterns; (c)–(f) CGI with pink noise speckle illumination using 800, 1500, and 5292 patterns. CGI with white noise is drastically blurred and totally indistinguishable even at full sampling (5292) due to the extremely strong background which even close to over exposure, while the CGI with pink noise still can retrieve the image; (h) MSE distribution with sampling numbers of 500, 800, 1500, 3000, 4500, and 5292. The dashed blue line and solid red line correspond to the evaluation of CGI results reconstructed by white and pink noise patterns, respectively.