Speaker
Description
Low-energy X-ray fluorescence (XRF) mapping at synchrotron radiation facilities [1, 2] is often limited by acquisition time and dose constraints [3], especially for sensitive samples such as biological specimens or cultural heritage objects. Compressive sensing strategies [3] offer a way to mitigate these limitations by enabling spatial undersampling or by triggering dynamical decisional mechanisms [3]. Still, reconstructions from these regimes are challenged by high noise, low photon counts, and incomplete data.
Traditional denoising, inpainting and reconstruction algorithms often fail under such low-count conditions, and iterative reconstruction pipelines require carefully tuned, handcrafted regularizers [4]. On the other hand, supervised deep learning methods - while powerful - pose risks of hallucinating details learned during training, which is especially problematic when ground truth is unavailable [5].
In this work, we propose a Bayesian Deep Image Prior (BDIP) framework for denoising and restoring XRF maps acquired at short dwell times [6, 7]. This method belongs to the class of unsupervised deep priors [5], requiring no pre-training, thus reducing the risk of introducing artificial features [7]. The approach [5] treats the reconstruction as an iterative optimisation problem, where a modified U-Net [8] fed with noise learns to generate a denoised image by progressively estimating the task-specific high-frequency content. Unlike conventional handcrafted priors that act as fixed filters or sparsity enforcers, the network learns a complex task-specific prior directly from the data.
A key advantage of the Bayesian formulation [7, 6] is its ability to estimate both epistemic uncertainty (reducible with more data) and aleatoric uncertainty (intrinsic to the noise) [9] via a variational method and Monte Carlo dropout [7, 10]. This results in pixel-wise uncertainty maps, providing insights into the reliability of the reconstructed signal [7]. Nonetheless, even if not fully immune to overfitting, BDIP provides more controlled convergence than conventional Deep Image Prior approaches [7].
We evaluated our method on XRF spectral maps measured at the TwinMic spectro-microscopy beamline [2] of the Elettra Synchrotron facility (Trieste) acquired from a 1 mm-thick sandstone sample treated with a nano-protective product [3, 11]. Due to the sample’s opacity, localisation was guided using only visible light and back-scattering images. Dwell times of 3 s and 0.1 s were used to simulate high and low-count scenarios. From the detected emission lines (Na, Si, and Al), Na, the weakest emitter, posed the most significant denoising challenge. Comparative benchmarks were performed using state-of-the-art methods such as calibrated [12] non-local-means [13], total variation [14], and wavelet [15] denoisers under a j-invariant framework [12]. Our method consistently achieved the highest SSIM scores [16], particularly in recovering fine details in the noisy Na map. Pixelwise uncertainty maps further highlighted regions of reconstruction instability, aiding interpretation.
References:
[1] Jenkins, R., Gould, R. W. & Gedcke, D. (1995). Quantitative X-ray Spectrometry. New York: M. Dekker.
[2] Gianoncelli, A., Kourousias, G., Merolle, L., Altissimo, M. & Bianco, A. (2016), Current status of the TwinMic beamline at Elettra: a soft X-ray transmission and emission microscopy station, J. Synchrotron Rad. 23, 1526-1537.
[3] Kourousias G, Billè F, Guzzi F, Ippoliti M, Bonanni V, et al. (2023) Advances in sparse dynamic scanning in spectromicroscopy through compressive sensing. PLOS ONE 18(11): e0285057.
[4] A. Levin, Y. Weiss, F. Durand and W. T. Freeman, "Understanding and evaluating blind deconvolution algorithms," 2009 IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, USA, 2009, pp. 1964-1971
[5] V. Lempitsky, A. Vedaldi and D. Ulyanov, "Deep Image Prior," (2018), IEEE/CVF Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA, 2018, pp. 9446-9454
[6] Z. Cheng, M. Gadelha, S. Maji and D. Sheldon, "A Bayesian Perspective on the Deep Image Prior," in 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA, 2019, pp. 5438-5446
[7] Laves, MH., Tölle, M., Ortmaier, T. (2020). Uncertainty Estimation in Medical Image Denoising with Bayesian Deep Image Prior. In: Sudre, C.H., et al. Uncertainty for Safe Utilization of Machine Learning in Medical Imaging, and Graphs in Biomedical Image Analysis. UNSURE GRAIL 2020 2020. Lecture Notes in Computer Science(), vol 12443. Springer, Cham.
[8] Ronneberger, O., Fischer, P., Brox, T. (2015). U-Net: Convolutional Networks for Biomedical Image Segmentation. In: Navab, N., Hornegger, J., Wells, W., Frangi, A. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015. MICCAI 2015. Lecture Notes in Computer Science, vol 9351. Springer, Cham.
[9] Alex Kendall and Yarin Gal. 2017. What uncertainties do we need in Bayesian deep learning for computer vision? In Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS'17). Curran Associates Inc., Red Hook, NY, USA, 5580–5590.
[10] Yarin Gal, Zoubin Ghahramani, Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning, Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:1050-1059, 2016.
[11] Raneri S, Giannoncelli A, Mascha E, Toniolo L, Roveri M, Lazzeri A, et al. Inspecting adhesion and cohesion of protectives and consolidants in sandstones of architectural heritage by X-ray microscopy methods. Materials Characterization. 2019; 156: 109853.
[12] J. Batson & L. Royer. Noise2Self: Blind Denoising by Self-Supervision, International Conference on Machine Learning, p. 524-533 (2019).
[13] A. Buades, B. Coll, & J-M. Morel. Non-Local Means Denoising. Image Processing On Line, 2011, vol. 1, pp. 208-212.
[14] A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, Springer, 2004, 20, 89-97.
[15] Chang, S. Grace, Bin Yu, and Martin Vetterli. “Adaptive wavelet thresholding for image denoising and compression.” Image Processing, IEEE Transactions on 9.9 (2000): 1532-1546.
[16] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13, 600-612.
| Workshop topics | Imaging theory |
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