In the process of image acquiring, often because of the fog, the features of information are not clear .This paper mainly studies the removal of fog from a single optical image covered by cloud.The research can effectively improve the utilization rate of acquired images, avoid multiple image acquisition, especially non-repeatable images, and greatly save the cost of image data acquisition;At the same time, it is conducive to improving the flexibility of remote sensing application, getting rid of the constraint of adverse climatic conditions, expanding the wide application of remote sensing technology in various fields, and providing useful information for military, meteorological, environmental, forestry, agriculture, geology and resources,

etc.It is also helpful to assist visual observation and prevent the occurrence of cloud weather accidents.

Due to the existence of cloud and fog in the atmosphere in the imaging process, remote sensing satellites often record the image data together with cloud and fog information, which affects the data quality and application effect.Cloud and fog have a great influence on visible and infrared radiation transmission energy, which changes greatly in space and time ,and is difficult to determine. It is one of the common noises in remote sensing optical

images.It affects the recognition of objects in the image, the classification of images, the accuracy of ground object information extraction, and even causes wrong results.The interpretation, analysis and use of remote sensing data are seriously affected.How to remove the influence of thin clouds and mist and extract surface information has become an important link to improve the utilization rate of remote sensing optical images.

Image pollution caused by cloud and fog mainly has two aspects:One is the non-gaussian random noise generated by the image of cloud particles themselves, which can be considered as additive noise;Secondly, the image blur caused by the scattering of light by cloud particles is the multiplicative noise of gaussian distribution.Especially when the fog is thick, additive noise dominates.

Remote sensing optical images usually need to be enhanced including correction processing, image transformation, image classification and other processing before being provided to users for use.
Correction processing.Image correction processing refers to the process of eliminating the distortion from the distorted image;The elimination of distortion in the amount of radiation is called radiation correction.Because people are used to using orthographic map, the distortion of remote sensing image must be corrected geometrically based on topographic map.Geometric correction steps are as follows:

(a) Select control points.Control points with the same name are selected on remote sensing image and topographic map respectively to establish the projection relationship between image and map. These control points should be selected where they can be clearly positioned.

(b) Establish the global mapping function.According to the geometric distortion property of the image and the number of ground control points to determine the correction mathematical model, the relationship between the image and the map space transformation is established.

© Resampling interpolation.In order to make the corrected output image pixel correspond to the input uncorrected image, the data of the input image is rearranged according to the determined correction formula.In the resampling, since the coordinates of the corresponding positions calculated are not integral values, the new pixel values must be obtained by interpolating the pixel values around.

In a summery.Radiation is directly related to the spectral reflectivity or spectral radiance of the target object based on the grayscale of the image obtained by the remote sensing device, and the measured values by the remote sensing device include the distortion caused by the atmospheric conditions such as the position and Angle of the sun, clouds and fog.These distortions must be eliminated in order to evaluate the reflection and radiation characteristics of the target.The process of eliminating all kinds of distortion attached to radiance in image data is radiative positivity.The result of radiation correction will change the hue and color of the image.