You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: A review on dark channel prior based image dehazing algorithms 
Chapter Title:  Dehazed image construction 
1. Abstract of Cited Paper (BIB001):  The sky region of restored images often appears serious noise and color distortion using classical dark channel prior algorithm. To address this issue, we propose an improved dark channel prior algorithm which recognizes the sky regions in hazy image by gradient threshold combined with the absolute value of the difference of atmospheric light and dark channel. And then we estimate the transmission in sky and non-sky regions separately. At last, we enhance the brightness and contrast of results. Experimental results show that our restored images are more natural and smooth in sky regions. 
2. Abstract of Cited Paper (BIB002):  Image has important applications in many fields such as marine surveillance, environment monitoring and so on. The scattering effects of the atmospheric particles in the air play a main role of resulting in contrast reduction and color fading. For dealing with this challenging but imperative issue, there are numerous researchers have strove for this scientific field and published a plenty of findings about restoring the foggy image. In generally, the foggy image always includes the sky and non-sky regions while the pixel values in this two distinguished regions is extremely different. The dark channel prior algorithm has been considered as one effective dehazing approach which only employs one constant factor for the overall image regardless of the scene pattern. This imprudent procedures always leads to more darkness image color and fails to achieve excellent results. For dealing with this challenging but imperative issue, we propose one improved dark channel prior dehazing approach using adaptive factor. In our algorithm, the foggy image is segmented into sky region and non-sky region respectively, the critical parameters i.e. light intensity and transmission ratio are obtained based on different factors. Some comparative experiments have also been conducted for validating dehazing performance of the proposed approach. 
3. Abstract of Cited Paper (BIB003):  In fog and haze weather conditions, the outdoor visibility is greatly reduced by the atmospheric scattering. Images taken in this weather suffer from serious degradation. Image dehazing based on the dark channel prior(DCP) is considered to be an elegant solution due to its advantages of simple implementation and excellent performance of dehazing. However, as it is based on the assumption that the transmission is locally constant, the patch size will affects the quality of dehazed images. A large patch size leads to bright atmosphere but serious halo artifacts, while a small one can achieve nice dehazing results with little halo artifacts but dim atmosphere. To achieve a nice dehazing reslut with little halo artifacts and good brightness atmosphere, an improved dehazing method based on the DCP and the guided filter(GF) was proposed in this paper. Our method differs from previous ones in two aspects. First, we take a small patch size(r d = 1) to solve the dark channel(DC), which can achieves a better contrast recovery with little halo artifacts compared to a middle one(r d = 7), then we proposed a brightness enhancement method on the dehazed image to solve the problem of dim atmosphere. Second, in the step of transmission optimizing, we take several gray scale images rather than the color hazy image as the guidance images. The experimental results show that the proposed method can achieve rather good dehazing results, but with a relative simple implementation and a low time complexity. 
4. Abstract of Cited Paper (BIB004):  The blurred image restoration method can dramatically highlight the image details and enhance the global contrast, which is of benefit to improvement of the visual effect during practical applications. This paper is based on the dark channel prior principle and aims at the prior information absent blurred image degradation situation. A lot of improvements have been made to estimate the transmission map of blurred images. Since the dark channel prior principle can effectively restore the blurred image at the cost of a large amount of computation, the total variation (TV) and image morphology transform (specifically top-hat transform and bottom-hat transform) have been introduced into the improved method. Compared with original transmission map estimation methods, the proposed method features both simplicity and accuracy. The estimated transmission map together with the element can restore the image. Simulation results show that this method could inhibit the ill-posed problem during image restoration, meanwhile it can greatly improve the image quality and definition.

Literature Review:
After estimating the atmospheric light Â and transmission mapt , the dehazed image J can be readily obtained from the degradation model as Eq.  . Specifically, J is given as where t 0 is a typical value for avoiding a low value of the denominator. Most DCP-based dehazing methods used t 0 as 0.1 [11-14, 20, 21, 25-27] . Figure 23 shows the dehazed images obtained using the top three transmission map refinement methods. As can be seen, the reconstruction of J by Eq. (28) can yield visually pleasant dehazed images. When the hazy image contains significant color distortion by abnormal climate such as sandstorm BIB001 , the estimated atmospheric light Â becomes far from achromatic, and thus, color correction is required at the dehazed image reconstruction. In such a case, J is obtained as follows: where the upper-script c represents the color channel, c ∈ {r, g, b}, and d c denotes the difference between the average values of the red and c channels of I. In other words, the offset in the red channel caused by sandstorm is subtracted before the construction of the dehazed image. Figure 24b , c shows the dehazed images obtained by using the same refined transmission map as shown in Fig. 22e but with Eqs. (28) and (29), respectively. The experimental results demonstrate the necessity of the color correction at the dehazed image construction stage. Equation BIB002 can also be easily extended to the images that appeared greenish or bluish due to other abnormal weather conditions or improper camera parameter settings. There are also several works considering the noise amplification problem during dehazed image construction BIB002 BIB003 . In addition, to obtain high contrast dehazed images, some image processing techniques can be applied including as linear stretching BIB004 , gamma correction BIB005 , and histogram specification  . Finally, Fig. 25 shows the time consumption of each dehazing step. Specifically, using the same experimental condition mentioned in Section 1.3.4, the average processing time of the 30 FRIDA test images was measured. The transmission map refinement step required the longest time when the bilateral and cross-bilateral filters were used, and the dark channel construction and transmission map estimation steps also required non-negligible time due to the block-min process in Eqs. (4) and (9).