High-quality compressed sensing imaging with limited detector bits using sparse measurements and multiple dithers

In recent years, compressed sensing (CS) imaging has emerged as a promising alternative to traditional imaging methods. One advantage of CS is that it uses post-processing algorithms to reconstruct the targets, and the sampling process does not have to obey the Nyquist sampling theorem. Moreover, it can collect the measured results using a single-point detector without spatial resolution. Owing to these advantages, CS imaging has found a wide range of applications in many fields, including spectral and fluorescence imaging.

Detectors used in imaging systems use a certain number of bits to perform analog-to-digital conversions. Such conversion processes often cause quantization errors. Thus, to obtain a high-quality image, a sufficiently high number of bits are needed to minimize the quantization-induced distortions. However, this also brings more problems, especially when low transmission speeds and a large amount of data are involved. With the high demand for the number of detector bits in CS imaging, addressing the challenges of quantization distortions has become more serious than ever. Therefore, it will be of great importance to realize high-quality CS imaging with limited detector bits.

Several techniques have been developed to minimize quantization errors in CS imaging using a limited number of detector bits. Among them is reducing the dynamic range of the signal with adaptive or balanced detection and employing post-processing algorithms to improve the image quality. Unfortunately, these methods are lack of universality for different types of  detectors. Interestingly, dithering (a random noise added to measured signals prior to quantization) has been identified as a promising method for reducing quantization errors.

Herein, a team of researchers from the Chinese Academy of Sciences: Fan Liu, Professor Xue-Feng Liu, Shen-Cheng Dou, Dr. Hu Li and Professor Guang-Jie Zhai in collaboration with Professor Xu-Ri Yao from Beijing Institute of Technology developed an improved compressive imaging method to obtain high-quality imaging with limited detector bits. This method was based on a combination of multiple dithers and sparse measurement strategies. A theoretical analysis of the relationship between reconstruction error and dynamic measurement range was performed. Their work is currently published in the journal, Optics Express.

The research team showed that the introduction of the sparse measurement matrix design played an important role in reducing the dynamic range of the measured signal. On the other hand, the multiple random dithers eliminated the fixed relationship between the input-output quantization and increased the effective dynamic range of detection, paving the way for quantization distortion reduction and improved reconstruction quality. As a result, the experiments and numerical simulations demonstrated that, unlike traditional CS imaging, the present system not only reduced the quantization distortion-induced reconstruction errors but could also realize preliminary imaging using only 1-bit detector.

Compared with classical CS imaging, the proposed method could effectively recover valid information even with a limited number of detector bits. In most practical applications, using low-bit detectors for data acquisition can reduce transmission and memory requirements. This is more advantageous in applications involving a large number of image pixels. In addition, low-bit detection is insensitive to small amounts of noise, which enhances the robustness of the imaging system. It was worth noting that even though a multi-point detector was utilized, there was no imaging relationship between the modulated target and the detector.

In summary, the authors reported a new CS imaging method with improved modulation and detection design capable of achieving high-quality images with a limited number of detector bits. The effect of the parameters and the detector noise was analyzed to validate the feasibility and applicability of the proposed method. It exhibited better detection capabilities and advantages over traditional CS imaging methods. In a statement to Advances in Engineering, Professor Xue-Feng Liu stated that their findings would inspire the application of CS imaging in different fields.