## 1 Introduction  
Image denoising is a very important part of image processing, and it is the basis of all subsequent processing, such as image recognition [1], object detection and tracking [2]. The denoising methods are mainly divided into spatial domain and transform domain filters. Spatial domain filters have high processing speed since they operate the pixels on the original images, such as median filter [3], wiener filter [4] and bilateral filter (BF) [5]. These algorithms can remove noise quickly, but the denoising abilities are mediocre. Transform domain filters are more robust since the images are transformed into another domain. Two major transform domain filters are Fourier transform (FT) [6] and wavelet transform (WT) [7]. WT overcomes the problem of FT that the window size is fixed, and does not change with frequency. Thus, WT gets better effect than FT. Discrete wavelet transform (DWT), proposed by [PERSON] [8], is widely applied in the image processing field. Dual-tree complex wavelet transform (DTCWT) proposed by [PERSON] in 1998 [9] can improve the DWT in several aspects. It owns three additional properties: approximate shift invariance, good directional selectivity, and limited data redundancy [10]. Recently, DTCWT has been used to eliminate the noise of images, and the method has been improved by many researchers. [PERSON] et al. [11] proposed a denoising method using the dual contourlet transform (DCT), which combined the directional filter bank (DFB) and DTCWT. The bivariate shrinkage function (BSF) with local variance estimation was adopted in [12] to process wavelet coefficients of DTCWT and the denoised images were reconstructed by the shrunk wavelet coefficients. Through changing the window size and shape of DTCWT, [PERSON] et al. [13] acquired good quality of denoised images. However, these methods cannot reach the best denoising performance since the parameters are fixed. Therefore, intelligent methods that search the best parameters through the optimization algorithm have been proposed by some researchers. In recent years, optimization problems are more and more extensive and many meta-heuristic algorithms has been proposed, such as genetic algorithm [14], ant colony algorithm [15], fish swarm algorithm [16], particle swarm algorithm [17], Virus colony search (VCS) algorithm [18], fire-fly algorithm [19], and so on. Among these algorithms, fruit-fly optimization algorithm (FOA), proposed by Professor [PERSON] in 2011 [20], has the advantages of simple structure, easy parameter setting, and fast convergence rate. Thus, FOA is widely used in economic management [21], forecasting [22], planning [23], etc. Nevertheless, similar to other optimal evolutionary algorithms, the original FOA may sink into local optima due to fixed fly step size. Meanwhile, the fitness function is a key problem that affects the denoising performance. Some researchers have put forward some examples. However, Most of them are full-reference. In practice, reference images cannot be acquired and these methods are not capable for practical usage. Moreover, the original thermal images cannot be used for analyzing because of the low sharpness, noise problem and inhomogeneous. Therefore, it is a significant task to create a method for thermal images that is capable of acquiring best image denoised performance without reference images. In this work, a non-reference image denoising method based on enhanced dual-tree complex wavelet optimized by fruit fly algorithm and bilateral filter (IFOA-DTCWT-BF) is proposed and the method is compared with DTCWT and other denoising algorithms. Some common objective indexes are used to analyze the performance of these algorithms. The rest of this paper is organized as follows. In Section 2, some related works are outlined based on the literature. In Section 3, the basic theories of DTCWT, FOA and bilateral filter are presented. In Section 4, the image denoising method based on IFOA-DTCWT-BF is elaborated, and a fly step range improved by inertia weight is performed.