###### Abstract  
Infrared (IR) Image preprocessing is aimed at image denoising and enhancement to help with small target detection. According to the sparse representation theory, the IR original image is low rank, and the coefficient shows a sparse character. The low rank and sparse model could distinguish between the original image and noise. The IR images lack texture and details. In IR images, the small target is hard to recognize. Traditional denoising methods based on nuclear norm minimization (NNM) treat all eigenvalues equally, which blurs the concrete details. They are unable to achieve a good denoising performance. Deep learning methods necessitate a large number of train images, which are difficult to obtain in IR image denoising. It is difficult to perform well under high noise in IR image denoising. Tracking and detection would not be possible without a proper denoising method. This article fuses the weighted nuclear norm minimization (WNNM) with an adaptive similar patch, searching based on the group sparse representation for infrared images. We adaptively selected similar structural blocks based on certain computational criteria, and we used the K-nearest neighbor (KNN) cluster to constitute more similar groups, which is helpful in recovering the complex background with high Gaussian noise. Then, we shrank all eigenvalues with different weights in the WNNM model to solve the optimization problem. Our method could recover more detailed information in the images. The algorithm not only obtains good denoising results in common image denoising but also achieves good performance in infrared image denoising. The target in IR images attains a high signal for the clutter in IR detection systems for remote sensing. Under common data sets and real infrared images, it has a good noise suppression effect with a high peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM), with higher noise and a much more complex background. IR image denoising; WNNM; group sparse representation; remote sensing 22 March 202322 April 20222 April 2022222 April 20  
include FFT filtering, butterworth filtering, bilateral filtering, and wavelet filtering. We can segment the noise spectrum and the useful signal spectrum with the above algorithms. As the noise spectrum is located all over the frequency, the signal still mixes the noise, and they cannot be completely segmented [5]. This article proposes the nonlocal mean filtering and uses nonlocal similarity to compose the Gaussian weight [6]. It can improve the resolution of the details and edges. Time-domain filtering contains the frame average filtering and weighted time-domain filtering. Several authors have risen the frame average filtering to protect the edge of the image [7]. This results in image trailing and blurring with the movement of the image. Other authors have considered the moving property and have completed the best match according to the moving trajectory [8]. Here, the trailing phenomenon was reduced. However, the method needs to finish the frame match with higher computation complexity. The traditional denoising algorithms are limited to concrete real IR images. Thus far, researchers have fixed their eyes on sparse representation [9]. The background is represented by an overcomplete dictionary with some sparse coefficients. We can extract the eigenvalue of the useful signal to restore the edges and detail texture in IR images [10]. This articleraises the sparse 3D transform-domain collaborative filtering (BM3D) to image denoising. This is more suitable for images with white Gaussian noise (WGN) with high time costs. Other researchers have given the solution to replace the \(l_{0}\) norm with \(l_{1}\) norm minimization [11]. This can decrease the hardship of the problem with a limited result [12]. It was proposed that the sparse representation can attain the eigenvector for reconstructing the original image. This method can recognize details and edges with a high level of complexity.