Infrared Image Enhancement Algorithm Based on Unsampled Contourlet Transform

With the rapid development of infrared technology, it has been widely used in many fields such as military defense, remote sensing detection, and non-destructive testing. Due to the imaging mechanism of infrared images and the infrared imaging system itself, the imaging effect of the infrared imaging system is not ideal. Most infrared images have the disadvantages of low contrast, blurred images, and narrow grayscale range. In practical applications, in order to improve the quality of infrared images, it is necessary to perform necessary enhancement processing on infrared images. The general image enhancement processing method is based on the spatial domain and the transform domain. The former mainly includes direct grayscale transformation, spatial filtering, and histogram processing; the latter transforms the image from the time domain to the frequency domain, and then enhances the image by correcting the coefficients in the transform domain. It is superior to the enhancement method based on the spatial domain. Representative algorithms include wavelet transform algorithms and contourlet transform-based algorithms [1].

In 2002, the Contourlet transform proposed by DO and VETTERLI is a very important type of multi-scale geometric analysis method. Contourlet can realize a "true" two-dimensional image representation and can extract very important intrinsic geometric structure features in the image. Similar to wavelet, which can be considered from the perspective of filters, Contourlet uses inseparable filters to establish a discrete multi-resolution multi-directional rate analysis to achieve flexible multi-resolution, local, and directional image representation. The direction selection ability and nonlinear approximation ability of Contourlet transform are studied, which shows that Contourlet transform has excellent performance beyond wavelet. However, since both wavelet transform and Contourlet transform lack translation invariance, the image enhancement result will produce pseudo-Gibbs distortion. The unsampled Contourlet transform proposed by CUNHA AL et al. has translation invariance and can suppress this distortion to a certain extent. This paper improves it. Compared with the image enhancement algorithms based on wavelet transform and Contourlet transform, this algorithm has achieved good enhancement effect [2].

1 Unsampled Contourlet Transform

Contourlet transform is also called pyramidal directional filter bank PDFB (Pyramidal Direction Filter Bank). The implementation of its decomposition transform can be divided into two steps: Laplacian Pyramid LP (Laplacian Pyramid) decomposition and directional filter bank DFB (Directional Filter Bank) filtering. The idea of ​​the transform is to use a basis function similar to a line segment to approximate the original image, thereby achieving sparse separation of the image signal. Therefore, to implement the Contourlet transform, it is first necessary to perform a multi-scale transform on the image to detect singular points at different scales, and then use a local directional transform to connect adjacent singular points at the same scale into a line segment structure [3]. The implementation process of the Contourlet transform can be summarized as follows:

(1) The image is subjected to a multi-scale transformation similar to wavelet to detect singular points on the edge;
(2) The image obtained in step (1) is subjected to a localized directional transformation to complete the detection of contour segments.

The non-sampled contourlet transform NSCT (Nonsubsampled contourlet transform) uses the non-sampled pyramid filter NSP (Nonsubsampled pyramid) to decompose the image into low-frequency and high-frequency parts, and then uses the non-sampled directional filter bank NSDFB (Nonsubasmpled Directional Filter Banks) to decompose the high-frequency part into several directions.

NSP is a translation-invariant dual-channel filter structure, which makes NSCT have multi-scale properties, and the filters of the next layer can be obtained by sampling the filters of the previous layer. Its frequency domain decomposition diagram is shown in Figure 1.

NSDFB is composed of two-channel non-sampled filter groups that are iteratively constructed. The filter groups are also not sampled and have translation invariance. NSDFB can decompose the high-frequency part obtained by the first-level transform into any power of 2 directions. The high-frequency part in each direction has the same size as the low-frequency part obtained by NSP and the original image. NSDFB decomposition is to expand the signal on a set of basis functions, and the corresponding basis functions are redundant [4]. The frequency domain decomposition diagram is shown in Figure 2.

The condition for NSP and NDFB to ensure complete reconstruction of the signal is that the filter must satisfy the equation:

where H0(z) and H1(z) represent the decomposition filters, and G0(z) and G1(z) represent the reconstruction filters. The undecimated Contourlet transform has the advantages of the Contourlet transform in expressing images, and also has translation invariance [4].

2 Image Enhancement Algorithm Based on Unsampled Contourlet Transform

After the image is transformed, the transformation coefficients are divided into three types: strong edge, weak edge and noise. Strong edge has larger coefficients in every direction; weak edge has large coefficients in one direction but small coefficients in other directions; noise refers to those coefficients that are small in all directions [5]. The enhancement function proposed by LAINE AF is:

x is the transformation coefficient of the input original image, and it is magnified again when 0

The process of the image enhancement algorithm based on Contourlet transform is shown in Figure 3, and the specific steps are as follows:

(1) Perform an unsampled Contourlet transform on the image to obtain transform coefficients at different scales and directions;
(2) Process the Contourlet transform coefficients according to the above principles;
(3) Reconstruct the enhanced image using the modified transform coefficients.

3 Experimental results and analysis

This paper uses the objective evaluation standard signal-to-noise ratio (SNR) to measure the objective quality of the denoised image after different denoising methods. The definition of SNR is as follows:

The experimental results are shown in Figure 4. The original image is an infrared photo taken by an infrared thermal imager with a resolution of 640×480 pixels. The building is the main detection target, and there is a small amount of vegetation behind the building. Figure 4(b) is a noisy image, Figure 4(c) is an image processed by Laplace transform, Figure 4(d) is an image processed by Contourlet transform, and Figure 4(e) is an image processed by the algorithm in this paper. The SNR values ​​are shown in Table 1.

As can be seen from Table 1, the SNR of the proposed algorithm is significantly improved, and the image visual is better, which is in line with the actual situation. The Contourlet transform method can capture the essential geometric characteristics of the image, and has better performance when expressing the singularity of various anisotropies, so it is better for processing images with rich texture information.