# Infrared Stripe Correction Algorithm Based on Wavelet Analysis and Gradient Equalization
## 1 Introduction  
Infrared imaging has been widely used in military, agricultural, and medical applications. However, owing to the defects of focal plane array materials and manufacturing limitations [1], the response of the infrared focal plane array unit is inconsistent, and serious spatial fixed pattern noise (FPN) is generated in the infrared image [2]. In engineering applications, people usually use traditional methods to correct FPN noise, in addition to FPN, random noise is also a part of the noise of the infrared image, and its energy is usually smaller than FPN. Random noise is composed of 1/f noise, thermal noise, bias voltage noise and so on. After the system is subjected to traditional non-uniformity correction, the FPN will be reduced, and random noise will become the main noise [3]. For uncooled infrared focal plane array (FPA), the FPA usually consists of a detector array, readout circuit and an analog-to-digital converter as shown in Figure 1a, where the non-uniformity of the readout circuit will also generate column FPN. Without certain noise compensation, the column FPN will appear as obvious vertical strips in a raw infrared image, as shown in Figure 1b [4]. To improve the quality of infrared images, stripe non-uniformity correction is required. Currently, the mainstream non-uniform correction (NUC) methods are calibration correction [5; 6] and scene-based correction [7; 8]. The calibration correction requires periodic interruption of the system's operation to eliminate the effects of temperature drift and then the calibration parameters cannot be updated in real time. The calibration correction generally handles non-uniformities caused by differences in response units and is not suitable for correcting stripe noise. By contrast, the scene-based correction does not require black body calibration, and extracts parameters based on scene information. As a result, it has attracted considerable attention. Scene-based correction may be either multi-frame or single-frame. The single frame method has a high convergence rate and can correct the stripe non-uniformity from the first frame. Currently, a single frame algorithm with better effect of removing stripe noise has been proposed by [PERSON] et al. namely an NUC algorithm based on grayscale inheritance [3]. However, it is difficult to determine an appropriate threshold; moreover, the algorithm is complex, which limits its applicability. [PERSON] et al. proposed a midway histogram equalization [9]. However, this method does not consider stripe noise characteristics, and thus the details and edge information of the image are blurred to some extent when the stripes are removed. Therefore, if the raw infrared image has low contrast, fuzzy results are obtained. [PERSON] et al. proposed a wavelet stripe correction algorithm [1], which performs a three-level size decomposition on the image and filters on each level. The algorithm is complex and the denoising effect is not ideal. [PERSON] put forward a method that minimizes the mean square error [10]. Although stripe noise is removed well, loss of image details often occurs. To resolve these issues, a new destriping algorithm that minimizes the horizontal gradient of the image is proposed in the present study. First, a wavelet transform is applied to the raw infrared image, and a Gaussian operator is used to convolve the cumulative histogram of the vertical component with a one-dimensional matrix to achieve gradient equalization in the horizontal direction. In addition, the vertical component is used as an input and a guided filter is used for double filtering, thus removing noise and simultaneously retaining image details. The main contribution of this research is to propose a multi-scale correction method. Firstly, the algorithm is based on the single frame image NUC algorithm, and thus does not need to process multiple frames of images and cause unnecessary \"ghosting\" problems.