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Deep learning-based image de-raining using discrete Fourier transformation

Analyzing behaviour of deep CNNs towards uncorrelated transformed domain data

Abstract

Single image rain streak removal is a well-explored topic in the field of computer vision. The de-raining problem is modeled as an image decomposition task where a rainy image is decomposed into rain-free background image and rain streek map. Unlike most of the existing de-raining methods, this paper attempts to decompose the rainy image in the frequency domain. The idea is inspired by pseudo-periodic characteristics of the noise signal (here the rain streaks) which leave some traces in the frequency domain, and the same can be utilized to predict the noise signal. In this paper, a deep learning-based rain streak prediction model is proposed which learns in discrete Fourier transform Oppenheim and Schafer (Discrete-TimeSignal Processing, Prentice Hall, Upper Saddle River, 1989) domain. To the best of our knowledge, this is the first approach where compressed domain coefficients are directly used as input to a deep convolutional neural network. The proposed model has been tested on publicly available synthetic datasets Fu et al. (in: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. https://doi.org/10.1109/CVPR.2017.186, Yang et al. (in: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. https://doi.org/10.1109/CVPR.2017.183), Yeh et al. (in: 2015 IEEE International Conference on Consumer Electronics-Taiwan, 2015. https://doi.org/10.1109/ICCE-TW.2015.7216999) and results are found to be comparable with the state of the art methods in the spatial domain. The presented analysis and study have an obvious indication to extend transform domain input to train the deep learning architecture especially image de-noising like problems.

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Notes

  1. DFT : Discrete Fourier Transformation.

  2. Figure 5a, e are first converted into YCbCr color space. Magnitude and phase are then calculated by performing DFT [25] on Y channel for each image. Chrominance values of Fig. 5a has been used to construct Fig. 5b, c. Chrominance values of Fig. 5e has been used to construct Fig. 5d.

  3. The quantitative analysis has been given in Appendix 6.1.

  4. Rain-streaks in this test-set may contradict with the real-rain.

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Acknowledgements

Authors would like to thank the anonymous reviewers for their insightful comments and suggestions. Authors would also like to acknowledge the funding agency, Ministry of Human Resource Development, Government of India.

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Appendix

Appendix

Quantitative analysis of rain-streaks present in Y channel compared to Cb & Cr

Deep learning models for image restoration, in RGB color-space due to its highly correlated nature, may induce white pixel artifacts and color saturation, especially in the case of image de-raining [30]. YCbCr is a more suitable color-space for image restoration when the noise in an image exhibits linear or a pseudo-periodic nature [24, 30]. To quantify the noise present in the Y channel compared to chrominance channels, we have adopted the concept of sparsity and conducted the following experiment on the test-set TD- Zhang et al. that consists of 1200 rainy-clean image pairs.

  1. 1.

    We convert the rainy and clean images into YCbCr color-space.

  2. 2.

    Obtains the pixel-wise difference between corresponding Y Cb Cr channels of rainy and clean images.

  3. 3.

    Measure the sparsity ratio based on the following equation

    $$\begin{aligned} \mathcal {S} = \frac{\text {No. of Zero-pixels}}{\text {Total No. of pixels}} \end{aligned}$$
    (19)
  4. 4.

    High sparsity indicates the low rain-noise present in the channel compared to its clean counterpart. We have obtained the following results. The same has been added in the appendix with qualitative results.

    Metric Y Cr Cb
    \(\mathcal {S}\) (avg.) 0.0449 0.4481 0.4040
  5. 5.

    It can be observed that the Y channel has the lowest sparsity ratio that indicates the highest rain-streak noise present compared to other channels.

  6. 6.

    Although the values are test-set specific, it may obey for any rain-streak removal test-set.

Run-time comparison

We have implemented the proposed model using Tensorflow framework [1]. It takes \(\sim \) 0.56 s to test an image of size \(512 \times 512\) on an 8 GB GPU. We have also compared the proposed model with existing schemes based on the run-time per image, and results are shown in Table 5.

Table 5 Run-time comparison of the proposed work with existing schemes

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Sharma, P.K., Basavaraju, S. & Sur, A. Deep learning-based image de-raining using discrete Fourier transformation. Vis Comput 37, 2083–2096 (2021). https://doi.org/10.1007/s00371-020-01971-w

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Keywords

  • Image de-raining
  • Deep learning
  • Convolutional neural networks
  • Discrete Fourier transformation