## 1 Introduction  
Achieving clear images of the objects embedded in turbid media has always been a challenge for biomedicine, nanotechnology and underwater imaging [1; 2; 3; 4; 5; 6; 7], as the scattering medium usually causes irregular scattering interference beams [8]. Though non-destructive coherent imaging methods [9; 10] with angle scanning and additional holographic reference light beam can help to solve the problem somewhat, the practical complex operations still hinder their real-time imaging applications. [PERSON] et al. proposed a single-shot coherent power-spectrum imaging method for imaging objects hidden by opaque scattering media [11] without angle scanning and additional holographic reference light, which may be a promising method for real-time scattering imaging.  
[PERSON]' s method could reconstruct object images hidden in scattering media with only a piece of the single-shot coherent power-spectrum pattern, which is a good attempt in real-time scattering imaging. However, for the practical captured power-spectrum pattern, the object images cannot always be successfully reconstructed quickly. The main factor causing this result is the setting of experimental conditions, including the roughness of the scattering layer, the accuracy of the power-spectrum pattern, the exposure time of the acquisition spectrum, and so on. In terms of algorithm, the feedback coefficient \(\beta\) is an important value, which can reduce the iteration error and accelerate the convergence of the algorithm. Many researchers set the feedback coefficients as an empirical constant, but the value of \(\beta\) will greatly change the process of object reconstruction, its selection is closely related to the experimental conditions, current literature have not studied whether the feedback coefficients need to be adjusted when the experimental conditions are changed. The most significant variable affecting the scattering imaging process among the conditions is the exposure time. None of the above literature has studied the reconstruction effect with the power spectrum acquired with different exposure times, so no certain relationship between the feedback coefficient and exposure time has been uncovered, including [PERSON]'s work, which is only a feasibility experimental verification. The fact is, the feedback coefficient \(\beta\) value for the hybrid input-output (HIO) reconstruction algorithm has to be carefully selected from a wide range of 0.5-1.0 which [PERSON] suggested [12], and even go through 0.1-2.0, so as to achieve the optimum reconstruction, which seriously reduces the reconstruction efficiency. Actually, even under the same experimental conditions, the exposure levels of various captured power-spectrum patterns will be different for various camera's exposure time settings, which then makes the information distribution of the patterns different. Therefore, the fixed single feedback coefficient \(\beta\) value cannot efficiently serve for the single-shot power-spectrum imaging method to reconstruct object images from the power-spectrum patterns with different exposures efficiently [13; 14; 15].  
Herein, we find that the optimum \(\beta\) value is closely related to the exposure degree of the captured power-spectrum patterns, which is not always limited in the range of 0.5-1.0. Furthermore, we analyze the relationship between the \(\beta\) values and the exposure conditions, which will be described in detail as an equation in Section 4, so as to improve the single-shot coherent power-spectrum imaging method for different exposure conditions by selecting suitable \(\beta\) values adaptively. We found that, for the underexposure, moderate exposure and overexposure cases, the optimum \(\beta\) value could be quickly selected from various narrow ranges, which promotes the rapid and accurate object reconstruction.