The single image dehazing algorithms in existence can only satisfy the demand for dehazing efficiency, not for denoising. In order to solve the problem, a Bayesian framework for single image dehazing considering noise is proposed. Firstly, the Bayesian framework is transformed to meet the dehazing algorithm. Then, the probability density function of the improved atmospheric scattering model is estimated by using the statistical prior and objective assumption of degraded image. Finally, the reflectance image is achieved by an iterative approach with feedback to reach the balance between dehazing and denoising. Experimental results demonstrate that the proposed method can remove haze and noise simultaneously and effectively.
As one of the most important topics and basic issues in image processing, single image dehazing aims at two aspects. One is creating visually pleasing images suitable for human visual perception; the other is improving the interpretability of images for computer vision and preprocessing tasks. Thus, advanced techniques of single image dehazing are in urgent needs. The existing papers can be roughly classified into two methods. The first scheme based on image enhancement technique aims at improving the visual effect of image directly, such as gamma correction [
By analyzing the recent dehazing algorithms based on image restoration, we find that most algorithms only consider improving contrast and luminance of degraded image; however, in fact, noise is a universal phenomenon and a significant issue in dehazing [
In this paper, we propose a novel “Bayesian framework,” which would avoid dynamic range compression in He’s algorithm. The accuracy of the input image is ensured by removing haze and noise simultaneously. The robustness of our approach is guaranteed by the iterative approach with feedback. This paper is arranged as follows. Section
The single image dehazing algorithm was classified as an image enhancement technique in the earlier time. Middleton [
As is well known, the image received by a sensor from scene points is often absorbed and scattered by a complex medium. In computer vision and atmospheric optics, the McCartney’s atmospheric scattering is playing a major role in image degradation. It was modeled as follows [
Noise from environment and sensor is also an important degradation factor, but it is not considered in McCartney’s atmospheric scattering model. Therefore, our improved atmospheric scattering model is proposed as follows:
The key to our approach is that it combines the best of the Bayesian framework, the statistical prior and objective assumption of degraded image, and the iterative algorithm with feedback, to achieve the balance between dehazing and denoising. This section arranges as follows. The establishment of dehazing based on Bayesian framework is in Section
Rearranging (
In order to keep (
Assuming that the signal and the noise are uncorrelated, the variance of (
The noise level can be estimated easily if we can decompose the minimum eigenvalue of the covariance matrix of the noisy patches as (
After analyzing 200 randomly selected haze images and their hazefree images, we can find that the distribution of chromaticity gradient histogram of haze images is the same as their hazefree images, which is the power of the exponential power distribution. In order to explain this, we can define the chromaticity of input image
Distribution of chromaticity gradient histogram. Top: the haze image. Bottom: the hazefree image (the horizontal gradient is shown in the figure; the vertical gradient has the same character as it). (a) The haze image and its hazefree image [
Results of MSE. Top: the haze image. Bottom: the hazefree image. (a) Example for images in our haze and hazefree image database and (b) the MSE between the distribution of chromaticity gradient histogram and their exponential power distribution of the 200 haze images and their hazefree images.
Therefore,
Human visual system (HVS) has specific response sensitivity to the small interval of light wavelength [
The sensitivity of green wavelength. (a) Photonic and scotopic response of the HVS [
In order to meet the global spatial smoothness of the image, which is the basic assumption of the atmospheric transmission map, meanwhile, to preserve the detailandedge information of
Putting the likelihood of (
Optimizing (
When solving (
The iterative approach with feedback based on the law of minimum noise level, where
Figures
Natural images to test performance. (a) Input, (b) the contrast experiments (from top to bottom: He’s result [
The enlargement of the area outlined in white of Figure
The relation curves. (a) The relation curve between numbers of iteration and noise level and (b) the relation curve between numbers of iteration and PDCP.
In order to validate the performance of our approach, 4 groups of experiments are established: synthetic images with haze and noise to test performance in Figure
Synthetic images with haze and noise to test performance. (a) Input [
Close depth images to test performance. (a) Input, (b) top: He’s result [
Close depth images with noise (0.2) to test performance. (a) Input, (b) top: He’s result [
Deep depth images to test performance. (a) Input, (b) top: He’s result [
The enlargement of the area outlined in white of Figure
Figure
The PSNR of Figure
Figure 
Figure 
Figure 
Figure 
Figure 


61.4638  64.1724  63.4186  61.2034 

We compare the proposed algorithms with different condition in Figures
Figures
The objective evaluation. (a) Noise level and (b) PDCP.
In this paper, we present a novel single image dehazing approach considering noise based on Bayesian framework. We focus on an improved atmospheric scattering model by considering noise and haze simultaneously. The likelihood of posterior probability based on Bayesian framework is estimated by the statistical prior and objective assumption of degraded image. Meanwhile, we focus more on the efficiency by choosing the transmission map to get the scene radiance. BM3D is used to fix the initial input of the iterative approach with feedback, which can help to achieve the balance between dehazing and denoising. The experimental results demonstrate that our approach is effective, especially in challenging scenes with both haze and noise. However, color distortion still exists which will be involved in our future work.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by National Natural Science Foundation of China (Grants no. 61372167, no. 61379104, no. 61203268, and no. 61202339).