Filtering techniques eliminate Gaussian image noise

Noisy images create problems in machine vision applications. Spatial filtering methods for removing noise have existed for more than a decade, but face problems like over smoothing without any preservation of edges, gradient reversal artifacts, ringing artifacts, and shift variance.

For machine vision and imaging tasks, the first step in finding eventual success is getting the highly informative image. Many types of noise exist, including salt and pepper noise, impulse noise, and speckle noise, but Gaussian noise is the most common type found in digital imaging. Within digital imaging, Gaussian noise occurs as a result of sensor limitations during image acquisition under low-light conditions, which make it difficult for the visible light sensors to efficiently capture details of the scene (see Fig. 1).

Newer filtering methods like block-matching and 3D filtering (BM3D), nonlinear means (NLM) filtering, and Shearlet transform prove more effective than previous methods used to remove noise. Spatial filtering techniques modify the spatial features of an image. A spatial filtering kernel helps facilitate spatial filter implementation. Convolution of a smoothing kernel with the desired noisy images produces a denoised image. Based on the property of these kernels, different denoising results can be obtained. For example, a Gaussian kernel is obtained by plugging in different space values for x and y into the equation,¹ and by controlling the value of sigma, the degree of smoothing can also be controlled.

Uniform image smoothing represents the main problem encountered with primitive filters, as doing so results in compromised important details.⁸ Introducing range parameters into the Gaussian equation helps avoid the smoothing operation at the edges and contours and thus solve the problem. Using this filter—a bilateral filter⁹—introduces artifacts into the resulting image. However, a guided filter offers a more effective, edge aware spatial filtering approach. This filter uses a guidance image to effectively smooth consistent pixel intensity areas while retaining important detail information with the help of a guidance image. This filter is effective in removing artifacts.¹⁰ Another filter effective in removing artifacts while preserving semantically meaningful information is the anisotropic diffusion filter, which uses second order partial differential equations with necessary parametric variations for smoothing.⁷

On the other hand, transforms use orthonormal filter banks to decompose images into low frequency and high frequency sub-band images. The low-frequency information contains the uniform pixel intensity areas and high frequency information contains all the edges and contours present in the image. A transform is considered effective in separating information if it can extract edges and contours out of multiple directions in the image. For example, a wavelet transform extracts high frequency information in three directions—horizontal, vertical, and diagonal—whereas the Shearlet transform extracts information in multiple directions.

Gaussian noise affects higher frequencies. Applying a thresholding operation to high frequency (detail) sub-bands eliminates noise. As transforming an image takes it into another domain, coefficients are obtained as a result. To retrieve original pixel intensities, inverse transform applies to these modified coefficients, a process that lays down the complete picture of denoising more comprehensively because of its information separation strategy.^{2, 11}

NLM filtering, weighted least square (WLS) filter, and BM3D filtering represent more sophisticated strategies for achieving better results. In WLS filtering, the weighted least square energy function is minimized to obtain the output, so in this strategy, recursive filtering applies to the noisy image. This filter is fast and effective in removing halo artifacts.¹³ NLM filters prove more effective in removing the outliers and mainly, shot noise. The nonlinearity of these filters helps to effectively remove the background noise while preserving meaningful information.⁸

For experimentation, a mobile device camera with dual camera setup with 12 Mpixel camera sensor and 13 Mpixel depth sensor for emphasizing objects in a scene provides images. Images in Figure 3 show the results of a standard image of a house contaminated by Gaussian noise of different standard deviation (sigma). In this experiment, images with Gaussian noise with sigma 30 are used. When higher sigma noise is added, the image gets more distorted and more difficult to recover (see Fig. 5). For testing, the two most popular and widely used metrics evaluate the performance: peak signal-to-noise ratio (PSNR) and mean square error (MSE): The two metrics can be explained as follows:

The higher the MSE value, the lower the denoised image quality. Hence, lower value of MSE indicates good denoising technique performance.

The table shows the values of PSNR and MSE for various denoising techniques. The metrics values can be compared with the visual results of various denoising techniques (see Fig. 6). Some state-of-the-art techniques like block-matching and 3D filtering (BM3D), nonlinear means filter, and Shearlet transform perform best among all techniques.

When compared to the original image, the visual results tend to lose some details, but the freedom of choosing parameters for the degree or smoothing provides flexibility for using these techniques in disparate applications.

Noise impacts the higher frequencies of an image, so the thresholding operation is only applied to the high-frequency layers. All spatial filters employed to remove noise remove higher frequencies present in the image. As the important edge and contour information is also high frequency information, a spatial filter or transform must remove noise without affecting the relevant edges and contours. All spatial filters or transforms proposed through the years have tried to solve this problem,^3-5 but BM3D, nonlinear means filter, and Shearlet transform perform best.

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