Authors:
(1) Hyosun Park, Department of Astronomy, University of Yonsei, Seoul, Republic of Korea;
(2) Yongsik Jo, Higher School of Artificial Intelligence, Unit, Ulsan, Republic of Korea;
(3) Seokun Kang, Higher School of Artificial Intelligence, Unit, Ulsan, Republic of Korea;
(4) Taehwan Kim, Higher School of Artificial Intelligence, Unit, Ulsan, Republic of Korea;
(5) Mr. James Jee, Department of Astronomy, University of Yonsei, Seoul, Republic of Korea and department of physics and astronomy, University of California, Davis, CA, United States.
Ties
Summary and 1 Introduction
2 method
2.1. Presentation and 2.2. Coder-Decoder architecture
2.3. Transformers for the restoration of the image
2.4. Details of the implementation
3 data and 3.1. HST data set
3.2. Gallsim data set
3.3. JWST data set
4 results of the JWST test data set and 4.1. PSNR and SSIM
4.2. Visual inspection
4.3. Restoration of morphological parameters
4.4. Restoration of photometric parameters
5 Application on real HST and 5.1 images. Restoration of single-time images and comparison with multi-epoch images
5.2. HST Multipoch image restoration and comparison with Multi-Epoch JWST images
6 limitations
6.1. Degradation of the quality of the restoration due to a high noise level
6.2. Punctual source recovery test
6.3. Artifacts due to the correlation of pixels
7 conclusions and thanks
Annex: A. Image restoration test with noise images only
References
6. Limits
6.1. Degradation of the quality of the restoration due to a high noise level
Although our in -depth learning model based on transformers offers advanced performance in improving resolution and noise reduction for moderate noise levels, inevitably, appropriate restoration becomes impossible when the noise level exceeds a certain threshold.
Figure 11 shows four of these examples. The upper row illustrates a case, where the distinct spiral arm in the GT image is not restored. When examining the corresponding LQ image, we believe that the loss of information due to noise is too important to refer to the presence of the arm in a spiral. The second line shows a case where the GT image's position angle is not properly restored. Again, we suspect that the LQ image is too noisy to allow an appropriate inference of the GT image angle. The third row is an example, where the ellipticity of the RS image is much more round than that of the GT image. In the last row, we illustrate a case, where the in -depth learning model does not reveal the two distinct peaks of the GT image.
Since the exact definition of restoration failure is a subjective question, it is difficult to quote an exact threshold. However, from visual inspections, we suggest that the frequency of failure increases significantly when the RMS value (after min-max normalization) of the LQ image is greater than ∼0.1.
6.2. Punctual source recovery test
In principle, the perfect deconvolution algorithm must restore a punctual source towards a Delta function, which is infinitely smaller than a pixel. In the traditional deconvolution in the field of Fourier, it is a difficult task because the operation is digitally unstable. The resulting images often have many ringing effects around a shiny central peak.
Since we have excluded the stars from the set of training data, our in -depth learning model has not explicitly learned to deconvolve the images of punctual source. Thus, it is interesting to examine how our learning model in depth, formed with only galaxy images, to restore the occasional sources. We carry out a punctual source recovery test as follows. First of all, we created 1,000 JWST quality GT star images. Because we have not deleted the PSF JWST from the set of training data, Star GT images should not look like a Delta Functions but the JWST PSF. We implemented it by involving a single pixel with a Gaussian whose size of the nucleus corresponds to the JWST PSF. Note that we random the stars positions in the 24 × 24 central pixels of Images 64 × 64. Then we created their LQ versions by further inviting GT images with HST PSF and adding noise. Finally, these LQ images are restored by our deep learning model. To study the systematic effect, we empower the 1,000 GT and RS images separately after having aligned their centers.
Figure 12 shows that the difference is subtle when we visually compare the GT (left) and RS batteries (middle). However, the residual image (right) illustrates that the PSF of the RS battery is systematically larger. Thus, we conclude that our in -depth learning model, drawn only with galaxy images, works less than ideal for punctual sources.
6.3. Artifacts due to the correlation of pixels
In our generation of LQ images, we assume that the noise is Gaussian. However, in real astronomical images, especially when we create deep images by stacking many truncated exhibitions, there are significant interpixel correlations. We note that these correlations of inter-pixel noise create significant artifacts.
Figure 13 displays some examples of these artefacts. The LQ images here are sampled from multi-epoch watered images. The presence of correlated noise is apparent
even from visual inspection. RS images show that the correlated noise creates certain artifacts of brightness on a low surface in the periphery of the galaxy, which are however absent in JWST images. The resolution of this problem could involve strategies such as the use of a different watered nucleus for the stack of images or taking advantage of the more advanced in -depth learning algorithms. Exploring these solutions will be a key objective of our future work.
