BCH Coding Assisted Imaging

TL;DR

An innovative approach by integrating Bose-Chaudhuri-Hocquenghem (BCH) error control coding (ECC) into CGI systems to assist imaging improves image quality across various signal-to-noise ratio (SNR) conditions.

Abstract

In modern correlation imaging systems, also known as ghost imaging (GI), particularly under low-light or noisy conditions, preserving high image fidelity presents a significant challenge. This paper introduces an innovative approach by integrating Bose-Chaudhuri-Hocquenghem (BCH) error control coding (ECC) into CGI systems to assist imaging. By encoding target image with BCH codes and using order-statistic decoding (OSD) for error correction during reconstruction, this approach significantly improves image quality across various signal-to-noise ratio (SNR) conditions. Simulation and experiment results validate that BCH coding assisted imaging achieves significantly enhanced robustness against additive white Gaussian noise (AWGN) and improved image reconstruction quality. In addition, the imaging performance of different BCH codes varies, with each code exhibiting distinct advantages based on factors such as code length and coding efficiency.

Figures (8)

• Figure 1: The BCH-based imaging system is an evolution of the correlation imaging system and shares similarities with a digital communication system. (a). Second-order correlation GI system. (b). BCH-based imaging system. (c). A block diagram of a digital communication system and a BCH-based imaging system. Both systems include an information source, corresponding to the data source in a communication link and the target in an imaging system. In each case, information is conveyed through a channel — an engineered communication channel in the former and physical optical propagation in the latter. The transmitted information is then captured by a receiver (communication) or a BD (imaging) and subsequently processed to recover the original data stream or reconstruct the target image.
• Figure 2: An example of imaging with BCH (31, 16) involves the generation of a speckle field using a DMD, which is determined by the generator matrix of the BCH code. The speckle field illuminates the target, and the total intensity of the target-modulated signals is collected by BD. This process integrates the principles of BCH coding with imaging.
• Figure 3: The PDF of the received signals and its remapping rules. (a) Find two closest integers to $\textit{i}_\textit{r}^{(n)}$. (b) The red and blue shaded regions correspond to the conditional probability $P_{i_t^{(n)}|i_r^{(n)}}$, with larger areas indicating higher probabilities; accordingly, $i_t^{(n}$ is restricted to the two most likely integer values, denoted by $i_{rmax}^{(n)}$ and $i_{rmin}^{(n)}$. For example, at $\textit{i}_\textit{r}^{(n)}=3.24$, the log-likelihood ratio satisfies $\ell^{(n)}<0$. As a result, $\textit{i}_\textit{r}^{(n)}=3.24$ is mapped to the bit value 1.
• Figure 4: The performance of BCH (31, 16) imaging versus the OSD theoretical prediction, shown in linear scale in (a) and logarithmic scale in (b). When the BD SNR exceeds $9\,\mathrm{dB}$, the simulations indicate that BCH (31, 16) achieves error-free reconstruction of the target.
• Figure 5: (a). Bit (pixel) error-rate performance of different BCH-based imaging schemes, indicated by four color-coded curves. (b). Reconstruction PSNR, quantifying the reconstruction quality for the four BCH-based imaging schemes.