Although the nonlocal means (NLM) algorithm takes a significant step forward in image filtering field, it suffers from a high computational complexity. To deal with this drawback, this paper proposes an acceleration strategy based on a correlation operation. Instead of perpixel processing, this approach performs a simultaneous calculation of all the image pixels with the help of correlation operators. Complexity analysis and experimental results are reported and show the advantage of the proposed algorithm in terms of computation and time cost.
Digital image denoising has been a fundamental and challenging issue for several decades [
The algorithm of nonlocal means (NLM) filtering was proposed by Buades et al. [
Some solutions have been proposed to alleviate this high computation burden for weights’ calculation. Liu et al. proposed an approximation to the similarity of neighborhood windows by employing an efficient Summed Square Image (SSI) further combined with Fast Fourier Transform (FFT) [
In this paper, compared with the traditional NLM algorithm, in which the calculations of weights are by the pixel by pixel way, our proposed fast strategy was performed on the whole image. Specifically, correlation operators are applied to compute the differential image and lead to a straightforward shortcut to achieve all the weights. By doing this, a lot of redundancy computation can be successfully avoided. Thereby, the computation speed of NLM is improved.
This paper is organized as follows. In Section
The image denoising model for an image
From (
From the above observations, we can see that, for one specific central pixel
More precisely, for a block
Two adjacent pixels
To avoid repetitive computations of the pixel difference
To deal with the operation with the whole image
Compute the “differential image”
This step can be efficiently implemented via a correlation operator:
The introduced correlation kernel matrix and its corresponding
By means of (
Compute the “square image”
This step can be easily conducted by an elementwise square operation as follows:
Compute the “Gaussian weighted Euclidean distance image”
This step can also be implemented by a correlation as follows:
Compute the exponential Gaussian weighted Euclidian distance image
Then, repeat Steps
Compute the normalization factor image
Compute the weights
Compute the processed
Note that the computational cost of Step
The schematic representation of the symmetry property for weight calculation.
Thus, when we calculate the
Specifically, when the kernel
Next, when
In Steps
Intuitively, this can be observed in Figure
Therefore, the necessary translation operations in terms of
Note also that the differences between the proposed fast algorithm and the traditional perpixel NLM algorithm lie in Steps
The computational complexity of the proposed algorithm is analyzed in this section. We assume that FFT and Inverse Fourier transform (IFFT) need the same computational complexity. In general, the computational complexity of twodimensional FFT for an
Computing
Computing
Computing
The computational cost of
The computational complexity of different methods.
Methods  Multiplication operation number  Addition operation number 

Proposed method 


Method in [ 


Method in [ 


The
Image size 





65536  40.32  3 

262144  64  4 

1048576  101.59  5 
In this section, we assess the performance of the proposed algorithm by conducting experiments with the “Lena” image with size 512 × 512 (Figure
The “Lena” image test in the experiment.
We conduct quality assessment in terms of peak signal to noise ratio (PSNR) and structural similarity index measuring (SSIM) [
The experiments results are reported in Table
The experiment results with different methods.

PSNR  SSIM  Time (seconds)  

Method in [ 
Method in [ 
Proposed method  
10  33.35  0.89  306.74  31.51  4.86 
20  29.73  0.80  373.44  34.72  6.76 
30  27.96  0.77  556.84  41.07  10.74 
In this paper, we proposed a correlation based strategy to accelerate NLM algorithms. This method filters the whole image simultaneously instead of filtering pixel by pixel as the original NLM one. This new approach shows that both the computational complexity and the running time are greatly reduced when compared to the original NLM method [
Recently, the collaborative filtering algorithms, such as the BM3D algorithm (block matching and 3D filtering algorithm), which are extension of the general concepts of grouping and block matching from the NLM, have shown the superior denoising performance. These are described in [
Eventually, referring to Table
The authors declare that there is no conflict of interests regarding the publication of this paper. They also solidly confirm that the mentioned received grants in Acknowledgments did not lead to any conflict of interests regarding the publication of this paper.
This research was supported by National Basic Research Program of China under Grant 2010CB732503, by National Natural Science Foundation under Grants 81370040, 81530060, 31100713, and 61201344, and by the Qing Lan Project in Jiangsu Province.