dataesr/scientific-paragraphs-categorization huggingface dataset:
Digital holography is well adapted to measure any modifications related to any objects. The method refers to digital holographic interferometry where the phase change between two states of the object is of interest. However, the phase images are corrupted by the speckle decorrelation noise. In this paper, we address the question of de-noising in holographic interferometry when phase data are polluted with speckle noise. We present a new database of phase fringe images for the evaluation of de-noising algorithms in digital holography. In this database, the simulated phase maps present characteristics such as the size of the speckle grains and the noise level of the fringes, which can be controlled by the generation process. Deep neural network architectures are trained with sets of phase maps having differentiated parameters according to the features.
The disadvantage of the WFT2F is the processing time required to de-noise phase data including 1024 × 1024 pixels. It follows that one requires fast denoising processing for digital holographic interferometry. In order to achieve this goal, two directions must be considered. The first one is related to the modelling of the speckle decorrelation noise and will be not discussed in this paper. The second one is related to the use of artificial intelligence (AI) in order to increase the computation speed of the data processing. In  [6, 7] , we proposed accurate modelling of the speckle noise. The advanced modelling of the speckle decorrelation noise permits us to carry on realistic simulations of phase data. Indeed, with natural images, there does exist a wide diversity which permits us to efficiently train AI with a large number of parameters.
However, in the field of phase data processing in digital holography, the quantity and the diversity are strongly reduced. So far, it is not possible to obtain experimental phase data with speckle noise together with its clean version. That is the reason why realistic simulated data are required. Simulated phase data can thus be used for AI and deep learning based on convolutional neural network in order to address the processing of de-noising phase maps. Especially, the great interest in AI methods is that they may strongly decrease the processing time. Related works on residual learning and holographic image databases are presented in Section 2. The aim is to reduce the de-noising time while reaching good performances on unseen images. To do so, new databases for training, development and validation are presented in Section 3.
In  [3] , HOLODEEP, a database including 25 fringe patterns divided into 5 patterns and 5 different signal-to-noise ratios was generated with a realistic noise simulator  [17]  to foster the diversity of phase fringe patterns. To the best of our knowledge, this database is the only available for training a de-noiser adapted to our context, but has the disadvantage of simulating soft conditions in terms of fringe diversity, signal-to-noise ratio and speckle grain size. In  [18] , a DnCNN was trained for speckle denoising and reaches good performances compared to other de-noising advanced techniques on images recorded under soft conditions. A previous work  [19]  presented how light DnCNN (with small depth) are able to de-noise images from HOLODEEP with a nice compromise between computation cost and performance.
The advantage of fine-tuning a DnCNN pre-trained on natural images on phase images corrupted with speckle noise was also investigated. Considering the previous works in literature, the contributions of the present article are as follows: (i) the description of a new database designed to train and evaluate a residual network for speckle de-noising in severe conditions; (ii) the release of pytorch implementation which includes data loader and data augmentation; (iii) the evaluation of phase error performances obtained by several DnCNN networks trained on different subsets of images.
HOLODEEP Database In the previous paper  [19] , the authors presented a database, namely HOLODEEP, which includes five different types of noise-free phase fringe patterns. The database was considered for training the models and also for development. Each phase pattern of HOLODEEP was corrupted with realistic speckle noise having suitable statistics as described in  [3]. The speckle grain size is fixed to N s = 2. Associated with the noise-free fringe patterns, the simulator  [3]  generated five noisy fringe patterns controlled with an adjustment parameter (namely ∆). The five data were corresponding to signal-to-noiseratios (SNR) in the range  [3 dB-12 dB]. A total of 25 images sized 1024 × 1024 pixels were generated. This database was designed for speckle de-noising in soft conditions, with a small speckle grain size (two pixels per grain) and moderate signal-to-noise ratios.
Definitions In the present paper, networks are evaluated in terms of phase errors and generalization power defined as the "ability to perform well on previously unobserved inputs"  [20]. In order to properly evaluate the generalization power of the network, the database is usually split in three subsets. The training subset consists of images used to train the network (∼80%). The development subset is used to verify if the network do not over-fit on the training data and is used to tune hyper-parameters (number of epochs, batch size, learning rate, etc. ) (∼10%). Finally, the test subset is used to give the final performance of the trained network on unseen data (∼10%). This protocol ensures training and properly evaluating the neural networks: the images used to assess the model have not been seen by the network during the training stage.
Diversity of Conditions Compared to  [18] , a new database, namely DB128 in the following, was generated using the realistic simulator. Phase fringe patterns with various signal-to-noise ratio (SNR), different speckle grain sizes and fringe diversity were simulated. DB128 includes 128 images of phase fringe patterns sized 1024 × 1024 pixels. Input cosine SNRs in DB128 are in the range [-0. 2, 8] dB. Three different speckle grain sizes have been used to generate images, at N s = (2, 4, 6) pixels per grain. In order to train and test the deep learning model, DB128 has been split in three sets: a training database DB128-train with 94 images, a development database with 10 images and a testing database, named DB128-test with 24 images. Images of DB128-test devoted to the evaluation of the models are reported in Figure  1.
Note that a specific parameter ∆ is used in the simulation to increase the noise amount in order to simulate severe experimental conditions  [3, 18]. More precisely, database DB128 includes images that were generated to have a low input signal-to-noiseratio (less than 3 dB) and a speckle grain size up to six pixels per grain. The notion of "severe conditions" corresponds to the joint realization of these conditions that are found in a lot of phase maps of this database. DB128 generation was driven to cover a high diversity of interference fringes. To preserve this diversity, we decided to keep Ns and ∆ distributions in all subsets as shown in Table  1. In the end, 94 images were used to train the networks, while 24 images were used to evaluate the performances. Hyper-parameters and network optimizations have been carried out in previous work (see  [19] ).
Consequently, the development set is not used in the present experiments. The latter layer permits us to reconstruct the output noise. The de-noised image is obtained by calculating the difference between the input noisy image and the output noise. The L2 loss between the reference and the predicted pixel values is considered for the loss function. For the reader interested in the architecture, please refer to the DnCNN original model (https://github. com/wbhu/DnCNN-tensorflow (accessed on 14 April 2022)). In a previous work, two different depths for DnCNN have been investigated  [19]. We have shown that DnCNN with only four ConvBlocks can be adequate when training HOLODEEP benchmark database. The advantage of such light networks is that they are trained quickly and they do not require large memory during inference.
Implementation The implementation with Tensorflow was first considered and then adapted using the PyTorch framework (https://git-lium. univ-lemans. fr/tahon/dncnn-tensorflowholography/ (accessed on 14 April 2022)). In the original version, two main scripts were used: one for the patch generation, and one for the training and evaluation of the models. In order to foster the computation time, a dataloader is implemented instead of the patch generation script. The dataloader automatically extracts from original complete images a given number of patches, shuffles them, converts radian phases to cosine or sine images, and performs artificial data augmentation. Artificial data augmentation aims at creating more training data by the use of standard image transformations. This operation is performed directly on patches, and generally avoids over-fitting.
Challenger Algorithms In order to compare the deep learning approach written in Pytorch, several challenger de-noising algorithms were chosen from literature. So we did select four algorithms that previously demonstrated to be efficient in our context. These are: The block-matching 3D filter  [21]  (BM3D), the windowed Fourier transform  [22]  (WFT2F), the dual-tree discrete wavelet transform (DTDWT), which is a particular implementation of the dual-tree complex wavelet transform  [23]  and finally what we call DLSHIFT algorithm, which was our last deep learning based approach write in Matlab presented in a recent paper  [5]. The blockmatching 3D (BM3D) algorithm takes into account both local and non-local features of data and is built on the concept of grouping and collaborative filtering.
The DTDWT is built with a set of separable filters which make the algorithm computationally very efficient. DLSHIFT is residual deep learning based approach written in Matlab. The algorithm is based on a DnCnn model  [14]  which has been firstly trained with a database consisting of natural images. It then has been retrained with a second database of phase images with decorrelation noise using the simulator. The DLSHIFT algorithm combines the use of several iterations with a phase shifted procedure in order to get multiple realisations of a unique input phase map. This scheme allows performing as much as the WFT2F does with the the HOLODEEP database. In order to evaluate the efficiency of iterations of our Pythorch model, we compare three versions which are called DL_DB128, DL_DB128_2 and DL_DB128_3.
Protocol We have trained diverse DnCNN networks in order to investigate the impact of the diversity of the training database, the network depth (D parameter, i. e. , the number of ConvBlocks), the convolutional kernel size (C). To compare with our previous work, we trained DnCNN models with HOLODEEP images as our baseline model with D = 4; 16 ConvBlocks. In order to investigate how the diversity of the training data impacts model performances, we also trained DnCNN models with the entire DB128 (DB128-full) and the train set described in Table  1. The kernel size has also been studied (C = 16; 32; 64). However, a kernel sized 64 pixels produces significantly better results than lower sizes. Therefore, this parameter is set to 64 in the following. Training images sized 1024 × 1024 are cropped into 384 patches of size 50 × 50, randomly selected among all possible patches, and data augmentation is performed with add45transpose, thus augmenting four times the number of training patches.
However, light models can be relevant for real-time applications as they speed-up the de-noising process. Indeed, inference is almost four times faster with D = 4 (80 ms on a RTX600 GPU card) than D = 16 (310 ms). First, regarding the performances obtained on HOLODEEP (3rd column), it is evident that training and evaluating a model on the same database aims at the best results (∆φ = 0. 0391 rad). However, the model trained on DB128-train achieves very competitive results (∆φ = 0. 0437 rad) beside the fact that it is not trained on the same data used for the evaluation. Second, the performances obtained on DB128-full and DB128-test (columns 4 and 5) are almost similar. It shows that the way the full database is split along the two controlling parameters ∆ and N s conserves the diversity of the images.
Finally, when evaluating the DB128-test, the difference between models trained on DB128-full (∆φ = 0. 1320 rad) and DB128-train (∆φ = 0. 1290 rad) is very low. The results show that the model trained on DB128-train achieves a better performance than the model trained with the full database on both the same full database and the test subset. During the training stage, the models are optimized on patches of size 50 × 50, while during the evaluation, the full 1024 × 1024 images are evaluated. This mismatch could explain the differences between these two models. Nevertheless, the last model trained on 94 images has the advantage of being trained on different data. All these conclusions show the high generalization power of the network trained on DB128-train on both HOLODEEP and DB128-test evaluation databases.
It confirms the importance of a controlled diversity in the training images. A closer look to Figure  2  shows that loss calculated on the development set is much more variable across epochs when the model is trained on HOLODEEP than on the full DB128 database. This confirms the high generalization power and robustness to unseen data of a de-noiser network trained on DB128. Applying the de-noising process many times on a noisy image is also possible. The results of three successive process show that it is still possible to gain in performance up to 2 iterations: ∆φ = 0. 1290 rad (1 iteration), ∆φ = 0. 1194 rad (2 iterations) and ∆φ = 0. 1297 rad (3 iterations). Assessments of previous presented algorithms are reported in Figures  3  and 4. Figure  3  provides rankings of the seven algorithms for the four selected metrics evaluated on DB128test database.
It appears that WFT2F remains the best algorithms with a mean phase error of about 0. 09 rad. Previous evaluations have shown that this method achieved 0. 025 rad with the HOLODEEP database which was constituted only with phase maps degraded with speckle noise with two pixels per grain. The residual deep learning model DL_DB128 provides very close results with WFT2F. Particularly, the use of two iterations successively yields a phase error of 0. 12 rad. Then, DLSHIFT algorithm achieved no better phase error than 0. 16 rad due to the fact that this model had been trained with speckle grain of size 2. Finally, BM3D and DTDWT demonstrate that they strongly fail in that context. Similarly, the same comments can be made about ranking of Qindex and peak-to-valley metrics. Trends of metrics are reported in Figure  4.
Evaluation on Target Images In Figures  5  and 6  are reported examples of processing achieved with DL_DB128_2 and WFT2F. Examples show bad conditions of degradation from input SNR and speckle size characteristics. For both examples, we clearly assess the efficiency of deep learning based model with respectively a difference of phase error of 0. 06 rad and 0. 12 rad for image 7 and image 123 of DB128 database. That demonstrates that DL_DB128_2 appears to be the best algorithm to deal with severe conditions. From left to right and top to bottom: Noise-free phase, noisy input phase, de-noised phase with WFT2F and DL_DB128_2. Cosine input SNR is of 1. 78dB. Phase error with WFT2F is equal to 0. 52 rad. Phase error with DL_DB128_2 is 0. 39 rad.
Conclusions This paper focuses on the problem of the de-noising of holographic phase images and presents a deep learning based approach that is specific for strong speckle noise. We introduce a new database named DB128 to train a residual model so that it better processes diverse and severe noise conditions. Particularly, the severe conditions deal with very low input SNR below 0dB, and large speckle grains, typically more than four pixels per grain. The new database constituted with 128 phase fringe patterns sized 1024 × 1024 pixels is characterized by a large diversity of its features: fringe density, fringe orientation, input SNR, speckle size, and fringe curvature. Results demonstrate that the model trained with the new database outperforms the two-dimensional windowed Fourier transform method with phase maps which correspond to severe conditions.
To support the needs of practitioners regarding 3D geological modelling and uncertainty quantification in the field, in particular from the mining industry, we propose a Python package called loopUI-0. 1 that provides a set of local and global indicators to measure uncertainty and features dissimilarities among an ensemble of voxet models. Results are presented of a survey launched among practitioners in the mineral industry, enquiring about their modelling and uncertainty quantification practice and needs. It reveals that practitioners acknowledge the importance of uncertainty quantification even if they do not perform it. A total of four main factors preventing practitioners performing uncertainty quantification were identified: a lack of data uncertainty quantification, (computing) time requirement to generate one model, poor tracking of assumptions and interpretations and relative complexity of uncertainty quantification.
, 2012; Pakyuz-Charrier et al. , 2018). Combined with expert knowledge, initial datasets can be used to shape some assumptions and define plausible conceptual models but despite the importance of conceptual uncertainty on predictions  (Pirot et al. , 2015) , it is too often limited to the definition of a unique scenario  (Ferré, 2017). From a perspective on algorithms, some assumptions such as how to set parameter ranges are needed and this can greatly impact the definition of geological parameters  (Lajaunie et al. , 1997)  prior to running predictive numerical simulations. Another aspect that is not always considered is the uncertainty related to a spatially limited sampling. Unsampled locations suggest a high uncertainty about the spatial distribution of the model parameters (or values of the property field); this is why it is preferable to resort to spatial stochastic simulations (e.
, 2013). Although some indicators have been used or developed for specific studies or softwares  (Li et al. , 2014) , to the best of our knowledge, no independent uncertainty analysis tool applicable to both discrete and continuous property fields, combining local and global indicators is available to practitioners. To investigate the uses and practices of the minerals industry regarding modelling and uncertainty quantification, we recently conducted a survey among numerical modelling practitioners from industry, government and academia in the sector of exploration and production of economic minerals. In this paper, first we present the main results and interpretations from this survey, the questions of which are listed in Appendix A. Second, to answer some of these needs, we propose a set of indicators to quantify geological uncertainty over an ensemble of geological models, represented as regular grid voxets and characterised by lithological units in the discrete domain and their underlying scalar field derived from implicit modelling in the continuous domain.
The various indicators are illustrated with a synthetic case derived from a simplified Precambrian dataset of the Hamersley, Western Australia. The Python code called loopUI-0. 1  (Pirot, 2021a)  and the notebooks used to compute and illustrate these indicators are available at https://doi. org/10. 5281/zenodo. 5656151. ) is used only to build a prior ensemble of models; Data 2 (e. g. geophysical measurements) is used to reduce the number of models that can be considered. It is achieved by exploring the ensemble of prior models and selecting those that are more likely to reproduce Data 2 within a prescribed level of error.
cet. edu. au/personnel/, last access: 8 June 2022; https://www. cet. edu. au/members/), Loop, last access: 8 June 2022; researchers (https://loop3d. github. io/loopers. html, last access: 8 June 2022) and related networks. About 150 persons were given the opportunity to participate. The solicited participants were essentially based in Australia but from a number of nationalities, with interests in geological modelling for mining applications. They were either from the industry or academia, from junior to senior profiles. Respondents had the opportunity to complete the survey on paper, in a text file or online. A total of 35 responses were collected and anonymised. Of the responses seven concerned models at different scales, and when the second part of the survey was not clearly duplicated for each scale, the answers were considered with caution for each modelling scale.
At the Mine scale (< 1 km dimension, ∼ 10 m resolution), the objectives are to assist with near mine exploration, resource estimation, ore body localisation, drill targeting, operation scheduling and efficient mining, by characterising local structures and geometries of stratigraphy and mineralisation. In addition to fulfilling these various objectives, 3D models are useful to improve hydrogeological characterisation, to identify critical zones where more knowledge has to be gained, to allow for comparison between datasets and test internal consistency, scenarios and last but not least, for visualisation and communication. Q5. Data types used as input for geoscientific modelling are similar and complementary across scales. For instance, geological mapping, geophysical data (gravity, magnetics, electromagnetics, seismic), and geochemistry are useful at all scales even though the related measurements might inform about a regional trend.
4 ). Q7-9. Modelling steps, assumptions or geological interpretations are not recorded in one third of the cases. In most cases, assumptions and elements of the modelling process are described in metadata or in separate reports. In very few cases, specific procedures and tools are available to keep track of these. The respondents use a variety of software, platforms or programming tools to produce 3D geological models and further data integration. The lack of a coherent workflow introduces the potential for uncertainty, error and loss of precision when forced to translate data formats across multiple software platforms, in addition to the time lost that could otherwise be dedicated to solving the problem under question or exploring alternative hypotheses. Q10. Overall, the main limitations involved in 3D geological modelling are uncertainty underestimation due to In what follows we address one of the needs identified in the survey: the lack of tools to quantify and visualise uncertainty from an ensemble of 3D voxets (prior or posterior ensembles).
, 1997) , 2-point (geo)statistics G. Pirot et al. : loopUI-0. 1: uncertainty indicators (semi-variogram, Matheron, 1963) , multiple-point statistics (multiple-point histogram,  Boisvert et al. , 2010) , connectivity (Renard and Allard, 2013), wavelet decomposition (e. g. Scheidt et al. , 2015)  and topology (e. g. Thiele et al. , 2016). Some indicators are similar to exploratory data analysis techniques but here they are applied to model ensemble analysis. To illustrate the different indicators, inspired by a Precambrian geological setting, that is a simplified dataset from the Hamersley region, Western Australia, we generated synthetic ensembles of 10 model sets for 3 different scenarios. Each model set is composed of a lithocode voxet describing the lithological units (categorical variable), and of its underlying scalar field voxet (continuous variable).