Hyperspectral Data Cube Research Articles

Evaluation of Focus Measures for Hyperspectral Imaging Microscopy Using Principal Component Analysis.

An automatic focusing system is a crucial component of automated microscopes, adjusting the lens-to-object distance to find the optimal focus by maximizing the focus measure (FM) value. This study develops reliable autofocus methods for hyperspectral imaging microscope systems, essential for extracting accurate chemical and spatial information from hyperspectral datacubes. Since FMs are domain- and application-specific, commonly, their performance is evaluated using verified focus positions. For example, in optical microscopy, the sharpness/contrast of visual peculiarities of a sample under testing typically guides as an anchor to determine the best focus position, but this approach is challenging in hyperspectral imaging systems (HSISs), where instant two-dimensional hyperspectral images do not always possess human-comprehensible visual information. To address this, a principal component analysis (PCA) was used to define the optimal ("ideal") optical focus position in HSIS, providing a benchmark for assessing 22 FMs commonly used in other imaging fields. Evaluations utilized hyperspectral images from visible (400-1100 nm) and near-infrared (900-1700 nm) bands across four different HSIS setups with varying magnifications. Results indicate that gradient-based FMs are the fastest and most reliable operators in this context.

Lossless hyperspectral image compression by combining the spectral decorrelation techniques with transform coding methods

ABSTRACT This study explores the utilization of Binary Embedded Zero Tree Wavelet Algorithms (BEZW) to compress hyperspectral images. The primary goal is to enhance the representation of spectral data while minimizing storage and transmission requirements. The BEZW algorithm employs wavelet transformations to leverage both spectral and spatial redundancies found in hyperspectral data cubes. Its embedded zero tree structure ensures efficient encoding of small coefficients with minimal overhead. The study evaluates the performance of the BEZW method utilizing various hyper-spectral datasets and compression settings, comparing it to other compression techniques. The results illustrate that the BEZW algorithm offers a promising approach to hyperspectral image compression, achieving competitive compression ratios while preserving spectral accuracy. This makes it a valuable option for applications where efficient hyperspectral data storage and transmission are crucial. The research contributes to the field of hyperspectral imaging by introducing an effective compression method that enhances data accessibility, simplifying the utilization of hyperspectral data in resource-constrained environments.

Choledochal cancer region detection in hyperspectral images using U-Net based models

Cholangiocarcinoma (CCA) is a type of cancer that forms in the bile duct that carry digestive fluid from the liver. CCA is the primary form of liver cancer that affects population ranging from age 60 to 69 years. CCA is difficult to diagnose at an early stage. Hyperspectral (HS) imaging is an advanced imaging technique that combines spectroscopy with conventional imaging. HS imaging is an emerging field of study which can be used for early CCA detection. HS imaging involves capturing images across various spectral bands, which forms a three-dimensional data cube often called as hyperspectral data cube. In this study, we have utilized U-Net based models, namely U-Net and DenseUNet were used to perform semantic segmentation on the HS images of CCA tissues. A band selective approach was employed to derive a subset of meaningful bands based on the spectrum plot from the HS image. The HS images are further preprocessed with Principal Component Analysis (PCA). The models were further evaluated by computing the accuracy, AUC (Area under the ROC curve), sensitivity and specificity metrics. The proposed models, namely, U-Net and DenseUNet reported an overall accuracy of 73.47% and 77.09% respectively. The DenseUNet models outperforms the U-Net model on every evaluation metric. The proposed models were also compared with other state-of-the-art (SOTA) models trained on various HS dataset. This study explores the application of HS imaging in carcinoma detection. The findings of this study could be used for further enhancement of the approach.

Ultra-high-speed four-dimensional hyperspectral imaging

We propose, to the best of our knowledge, a novel deep learning–enabled four-dimensional spectral imaging system composed of a reflective coded aperture snapshot spectral imaging system and a panchromatic camera. The system simultaneously captures a compressively coded hyperspectral measurement and a panchromatic measurement. The hyperspectral data cube is recovered by the U-net-3D network. The depth information of the scene is then acquired by estimating a disparity map between the hyperspectral data cube and the panchromatic measurement through stereo matching. This disparity map is used to align the hyperspectral data cube and the panchromatic measurement. A designed fusion network is used to improve the spatial reconstruction of the hyperspectral data cube by fusing aligned panchromatic measurements. The hardware prototype of the proposed system demonstrates high-speed four-dimensional spectral imaging that allows for simultaneously acquiring depth and spectral images with an 8 nm spectral resolution between 450 and 700 nm, 2.5 mm depth accuracy, and a 1.83 s reconstruction time.

Hyperspectral dark-field microscopy of human breast lumpectomy samples for tumor margin detection in breast-conserving surgery.

Hyperspectral dark-field microscopy (HSDFM) and data cube analysis algorithms demonstrate successful detection and classification of various tissue types, including carcinoma regions in human post-lumpectomy breast tissues excised during breast-conserving surgeries. We expand the application of HSDFM to the classification of tissue types and tumor subtypes in pre-histopathology human breast lumpectomy samples. Breast tissues excised during breast-conserving surgeries were imaged by the HSDFM and analyzed. The performance of the HSDFM is evaluated by comparing the backscattering intensity spectra of polystyrene microbead solutions with the Monte Carlo simulation of the experimental data. For classification algorithms, two analysis approaches, a supervised technique based on the spectral angle mapper (SAM) algorithm and an unsupervised technique based on the -means algorithm are applied to classify various tissue types including carcinoma subtypes. In the supervised technique, the SAM algorithm with manually extracted endmembers guided by H&E annotations is used as reference spectra, allowing for segmentation maps with classified tissue types including carcinoma subtypes. The manually extracted endmembers of known tissue types and their corresponding threshold spectral correlation angles for classification make a good reference library that validates endmembers computed by the unsupervised -means algorithm. The unsupervised -means algorithm, with no a priori information, produces abundance maps with dominant endmembers of various tissue types, including carcinoma subtypes of invasive ductal carcinoma and invasive mucinous carcinoma. The two carcinomas' unique endmembers produced by the two methods agree with each other within residual error margin. Our report demonstrates a robust procedure for the validation of an unsupervised algorithm with the essential set of parameters based on the ground truth, histopathological information. We have demonstrated that a trained library of the histopathology-guided endmembers and associated threshold spectral correlation angles computed against well-defined reference data cubes serve such parameters. Two classification algorithms, supervised and unsupervised algorithms, are employed to identify regions with carcinoma subtypes of invasive ductal carcinoma and invasive mucinous carcinoma present in the tissues. The two carcinomas' unique endmembers used by the two methods agree to residual error margin. This library of high quality and collected under an environment with no ambient background may be instrumental to develop or validate more advanced unsupervised data cube analysis algorithms, such as effective neural networks for efficient subtype classification.

Enhancing Diagnostic Capabilities for Occupational Lung Diseases Using LIBS Imaging on Biopsy Tissue.

Laser-induced breakdown spectroscopy (LIBS) imaging continues to gain strength as an influential bioanalytical technique, showing intriguing potential in the field of clinical analysis. This is because hyperspectral LIBS imaging allows for rapid, comprehensive elemental analysis, covering elements from major to trace levels consistently year after year. In this study, we estimated the potential of a multivariate spectral data treatment approach based on a so-called convex envelope method to detect exotic elements (whether they are minor or in trace amounts) in biopsy tissues of patients with occupational exposure-related diseases. More precisely, we have developed an approach called Interesting Features Finder (IFF), which initially allowed us to identify unexpected elements without any preconceptions, considering only the set of spectra contained in a LIBS hyperspectral data cube. This task is, in fact, almost impossible with conventional chemometric tools, as it entails identifying a few exotic spectra among several hundred thousand others. Once this detection was performed, a second approach based on correlation was used to locate their distribution in the biopsies. Through this unique data analysis pipeline to processing massive LIBS spectroscopic data, it was possible to detect and locate exotic elements such as tin and rhodium in a patient's tissue section, ultimately leading to a possible reclassification of their lung condition as an occupational disease. This review will thus demonstrate the potential of this new diagnostic tool based on LIBS imaging in addressing the shortcomings of approaches developed thus far. The proposed data processing approach naturally transcends this specific framework and can be leveraged across various domains of analytical chemistry, where the detection of rare events is concealed within extensive data sets.

Hyperspectral push-broom imager using a volume Bragg grating as an angular filter.

A hyperspectral push-broom imager has been designed, constructed, and tested. The narrow angular selectivity of a weakly index modulated volume Bragg grating is utilized to replace the objective lens, slit, and collimating lens of a conventional slit-based hyperspectral push-broom imager. The imager comprises a dispersion grating, an angular filter grating, a focusing lens, and an image sensor. The imager has a field of view (FOV) of 17 degrees in the spatial direction, a spectral range from 400 nm to 900 nm, and a spectral resolution of 2.1 nm. The acquired hyperspectral data cubes are presented, and the influence of wavelength-dependent incident angle errors is analyzed.

Metasurface-empowered snapshot hyperspectral imaging with convex/deep (CODE) small-data learning theory

Hyperspectral imaging is vital for material identification but traditional systems are bulky, hindering the development of compact systems. While previous metasurfaces address volume issues, the requirements of complicated fabrication processes and significant footprint still limit their applications. This work reports a compact snapshot hyperspectral imager by incorporating the meta-optics with a small-data convex/deep (CODE) deep learning theory. Our snapshot hyperspectral imager comprises only one single multi-wavelength metasurface chip working in the visible window (500-650 nm), significantly reducing the device area. To demonstrate the high performance of our hyperspectral imager, a 4-band multispectral imaging dataset is used as the input. Through the CODE-driven imaging system, it efficiently generates an 18-band hyperspectral data cube with high fidelity using only 18 training data points. We expect the elegant integration of multi-resonant metasurfaces with small-data learning theory will enable low-profile advanced instruments for fundamental science studies and real-world applications.

Hyperspectral Image Compression Using Prediction-based Band Reordering Technique

The hyperspectral image represents various spectral properties Because it consists of broad spectral information of ground materials that can be used for various applications, These images are collected as large amounts of data that must be processed and transmitted to the ground station. These acquired images contain redundant spectral information that has to be reduced in order to reduce transmission and storage capacity. This work focuses on preserving their quality while compressing them using band reordering techniques and prediction coding. This can be accomplished by preprocessing in which sub-bands are decomposed and bands are reordered into unsequenced compression can be accomplished through using the technique of linear prediction. The report discusses the Pavia University hyperspectral image data cube, which was acquired via a sensor known as a reflected optics system imaging spectrometer (ROSIS-3) over the city of Pavia, Italy.

Automated Georectification, Mosaicking and 3D Point Cloud Generation Using UAV-Based Hyperspectral Imagery Observed by Line Scanner Imaging Sensors

Hyperspectral sensors mounted on unmanned aerial vehicles (UAV) offer the prospect of high-resolution multi-temporal spectral analysis for a range of remote-sensing applications. However, although accurate onboard navigation sensors track the moment-to-moment pose of the UAV in flight, geometric distortions are introduced into the scanned data sets. Consequently, considerable time-consuming (user/manual) post-processing rectification effort is generally required to retrieve geometrically accurate mosaics of the hyperspectral data cubes. Moreover, due to the line-scan nature of many hyperspectral sensors and their intrinsic inability to exploit structure from motion (SfM), only 2D mosaics are generally created. To address this, we propose a fast, automated and computationally robust georectification and mosaicking technique that generates 3D hyperspectral point clouds. The technique first morphologically and geometrically examines (and, if possible, repairs) poorly constructed individual hyperspectral cubes before aligning these cubes into swaths. The luminance of each individual cube is estimated and normalised, prior to being integrated into a swath of images. The hyperspectral swaths are co-registered to a targeted element of a luminance-normalised orthomosaic obtained using a standard red–green–blue (RGB) camera and SfM. To avoid computationally intensive image processing operations such as 2D convolutions, key elements of the orthomosaic are identified using pixel masks, pixel index manipulation and nearest neighbour searches. Maximally stable extremal regions (MSER) and speeded-up robust feature (SURF) extraction are then combined with maximum likelihood sample consensus (MLESAC) feature matching to generate the best geometric transformation model for each swath. This geometrically transforms and merges individual pushbroom scanlines into a single spatially continuous hyperspectral mosaic; and this georectified 2D hyperspectral mosaic is then converted into a 3D hyperspectral point cloud by aligning the hyperspectral mosaic with the RGB point cloud used to create the orthomosaic obtained using SfM. A high spatial accuracy is demonstrated. Hyperspectral mosaics with a 5 cm spatial resolution were mosaicked with root mean square positional accuracies of 0.42 m. The technique was tested on five scenes comprising two types of landscape. The entire process, which is coded in MATLAB, takes around twenty minutes to process data sets covering around 30 Ha at a 5 cm resolution on a laptop with 32 GB RAM and an Intel® Core i7-8850H CPU running at 2.60 GHz.

InSPECtor: an end-to-end design framework for compressive pixelated hyperspectral instruments.

Classic designs of hyperspectral instrumentation densely sample the spatial and spectral information of the scene of interest. Data may be compressed after the acquisition. In this paper, we introduce a framework for the design of an optimized, micropatterned snapshot hyperspectral imager that acquires an optimized subset of the spatial and spectral information in the scene. The data is thereby already compressed at the sensor level but can be restored to the full hyperspectral data cube by the jointly optimized reconstructor. This framework is implemented with TensorFlow and makes use of its automatic differentiation for the joint optimization of the layout of the micropatterned filter array as well as the reconstructor. We explore the achievable compression ratio for different numbers of filter passbands, number of scanning frames, and filter layouts using data collected by the Hyperscout instrument. We show resulting instrument designs that take snapshot measurements without losing significant information while reducing the data volume, acquisition time, or detector space by a factor of 40 as compared to classic, dense sampling. The joint optimization of a compressive hyperspectral imager design and the accompanying reconstructor provides an avenue to substantially reduce the data volume from hyperspectral imagers.

A Self-Supervised Anomaly Detector of Fruits Based on Hyperspectral Imaging.

Hyperspectral imaging combined with chemometric approaches is proven to be a powerful tool for the quality evaluation and control of fruits. In fruit defect-detection scenarios, developing an unsupervised anomaly detection framework is vital, as defect sample preparation is labor-intensive and time-consuming, especially for exploring potential defects. In this paper, a spectral-spatial, information-based, self-supervised anomaly detection (SSAD) approach is proposed. During training, an auxiliary classifier is proposed to identify the projection axes of principal component (PC) images that were transformed from the hyperspectral data cubes. In test time, the fully connected layer of the learned classifier was used as a 'spectral-spatial' feature extractor, and the feature similarity metric was adopted as the score function for the downstream anomaly evaluation task. The proposed network was evaluated with two fruit data sets: a strawberry data set with bruised, infected, chilling-injured, and contaminated test samples and a blueberry data set with bruised, infected, chilling-injured, and wrinkled samples as anomalies. The results show that the SSAD yielded the best anomaly detection performance (AUC = 0.923 on average) over the baseline methods, and the visualization results further confirmed its advantage in extracting effective 'spectral-spatial' latent representation. Moreover, the robustness of SSAD is verified with the data pollution experiment; it performed significantly better than the baselines when a portion of anomalous samples was involved in the training process.

Noise Robust Hyperspectral Image Classification With MNF-Based Edge Preserving Features

Hyperspectral image (HSI) classification is an important topic in remote sensing. In this paper, we improve the principal component analysis (PCA)-based edge preserving features (EPFs) for HSI classification. We select to use minimum noise fraction (MNF) instead of PCA to reduce the dimensionality of the hyperspectral data cube to be classified. We keep all the rest steps from the PCA-based EPFs for HSI classification. Since MNF can preserve fine features of a HSI data cube better than PCA, our new method can outperform PCA-EPFs for HSI classification significantly. Experimental results show that our new method performs better than the PCA-based EPFs under such noisy environment as Gaussian white noise and shot noise. In addition, our MNF+EPFs outperform the PCA+EPFs even when no noise is added to the HSI data cubes for most testing cases, which is very desirable in remote sensing.

A New Remote Hyperspectral Imaging System Embedded on an Unmanned Aquatic Drone for the Detection and Identification of Floating Plastic Litter Using Machine Learning

This paper presents a new Remote Hyperspectral Imaging System (RHIS) embedded on an Unmanned Aquatic Drone (UAD) for plastic detection and identification in coastal and freshwater environments. This original system, namely the Remotely Operated Vehicle of the University of Littoral Côte d’Opale (ROV-ULCO), works in a near-field of view, where the distance between the hyperspectral camera and the water surface is about 45 cm. In this paper, the new ROV-ULCO system with all its components is firstly presented. Then, a hyperspectral image database of plastic litter acquired with this system is described. This database contains hyperspectral data cubes of different plastic types and polymers corresponding to the most-common plastic litter items found in aquatic environments. An in situ spectral analysis was conducted from this benchmark database to characterize the hyperspectral reflectance of these items in order to identify the absorption feature wavelengths for each type of plastic. Finally, the ability of our original system RHIS to automatically recognize different types of plastic litter was assessed by applying different supervised machine learning methods on a set of representative image patches of marine litter. The obtained results highlighted the plastic litter classification capability with an overall accuracy close to 90%. This paper showed that the newly presented RHIS coupled with the UAD is a promising approach to identify plastic waste in aquatic environments.

Hyperspectral Classification of Hazardous Materials Based on Deep Learning

The identification of hazardous materials is a key measure in the prevention and control of fire and explosion disasters. Conventional techniques used to identify hazardous materials include contact detection and post-sampling laboratory testing, which cannot meet the needs of extreme environments, where personnel and equipment are not accessible for on-site detection. To address this problem, this paper proposes a method for the classification and identification of hazardous materials based on convolutional neural networks, which can achieve non-contact remote detection of hazardous materials. Firstly, a dataset containing 1800 hyperspectral images of hazardous materials, which can be used for deep learning, is constructed based on the hazardous materials hyperspectral data cube. Secondly, based on this, an improved ResNet50-based classification method for hazardous materials is proposed, which innovatively utilizes a classification network based on offset sampling convolution and split context-gated convolution. The results show that the method can achieve 93.9% classification accuracy for hazardous materials, which is 1% better than the classification accuracy of the original ResNet50 network. The network also has high performance under small data volume conditions, effectively solving the problem of low classification accuracy due to small data volume and blurred image data features of labelled hazardous material images. In addition, it was found that offset sampling convolution and split context-gated convolution showed synergistic effects in improving the performance of the network.

Hyperspectral image classification based on residual dense and dilated convolution

The approach based on Convolutional Neural Network model has been widely employed in the field of hyperspectral image classification, demonstrating promising classification performance. However, traditional CNN methods only extract deep features from the end of the network, without considering the combination of shallow and deep features from the network. Moreover, most methods extract features using fixed convolutional kernel, which cannot be changed according to the complex spatial structure of hyperspectral image, and ignore the features of data in spatial-spectral distribution. To solve the aforementioned issues, we propose a method for classifying hyperspectral image based on residual dense and dilated convolution (RDDC-3DCNN). First, our method uses a 3D convolutional neural network as the base structure, and the raw hyperspectral data cube is used as the input of the network. Then, a residual dilation dense block incorporating dilated convolution is devised, which enabled the extraction of spatial-spectral features from hyperspectral image using 3D dilated convolution, while simultaneously fusing spatial-spectral features from different levels. After that, shortcut connections is added into the designed module to fully combine the shallow features and deep features of the network. Finally, the fused features obtained are sequentially passed through fully connected layer, dropout layer, and softmax layer to accomplish classification. The experimental results show that the method achieved classification accuracies of 98.87%, 99.33% and 99.32% on the the Indian Pines, the University of Pavia and Salinas datasets, respectively. Experimental results indicate that the proposed RDDC-3DCNN method can make full extract of the spatial and spectral information of the image, and it has better performance than some advanced algorithms in HSI classification.

Ultra-high-resolution observations of plasmoid-mediated magnetic reconnection in the deep solar atmosphere

Context. Magnetic reconnection in the deep solar atmosphere can give rise to enhanced emission in the Balmer hydrogen lines, a phenomenon referred to as Ellerman bombs. Aims. To effectively trace magnetic reconnection below the canopy of chromospheric fibrils, we analyzed unique spectroscopic observations of Ellerman bombs in the Hα line. Methods. We analyzed a 10 min data set of a young emerging active region observed with the prototype of the Microlensed Hyperspectral Imager (MiHI) at the Swedish 1-m Solar Telescope (SST). The MiHI instrument is an integral field spectrograph that is capable of achieving simultaneous ultra-high resolution in the spatial, temporal, and spectral domains. With the combination of the SST adaptive optics system and image restoration techniques, MiHI can deliver diffraction-limited observations if the atmospheric seeing conditions allow. The data set samples the Hα line over 4.5 Å with 10 mÅ pix−1, with 0.​​″065 pix−1 over a field of view of 8.​​″6 × 7.​​″7, and at a temporal cadence of 1.33 s. This constitutes a hyperspectral data cube that measures 132 × 118 spatial pixels, 456 spectral pixels, and 455 time steps. Results. There were multiple sites with Ellerman bomb activity associated with strong magnetic flux emergence. The Ellerman bomb activity is very dynamic, showing rapid variability and a small-scale substructure. We found a number of plasmoid-like blobs with full-width-half-maximum sizes between 0.​​″1 and 0.​​″4 and moving with apparent velocities between 14 and 77 km s−1. Some of these blobs have Ellerman bomb spectral profiles with a single peak at a Doppler offset between 47 and 57 km s−1. Conclusions. Our observations support the idea that fast magnetic reconnection in Ellerman bombs is mediated by the formation of plasmoids. These MiHI observations demonstrate that a microlens-based integral field spectrograph is capable of probing fundamental physical processes in the solar atmosphere.

Classification of Fresh and Frozen-Thawed Beef Using a Hyperspectral Imaging Sensor and Machine Learning

The demand for safe and edible meat has led to the advancement of freeze-storage techniques, but falsely labeled thawed meat remains an issue. Many methods have been proposed for this purpose, but they all destroy the sample and can only be performed in the laboratory by skilled personnel. In this study, hyperspectral image data were used to construct a machine learning (ML) model to discriminate between freshly refrigerated, long-term refrigerated, and thawed beef meat samples. With four pre-processing methods, a total of five datasets were prepared to construct an ML model. The PLS-DA and SVM techniques were used to construct the models, and the performance was highest for the SVM model applying scatter correction and the RBF kernel function. These results suggest that it is possible to construct a prediction model to distinguish between fresh and non-fresh meat using the spectra obtained by purifying hyperspectral image data cubes, which can be a rapid and non-invasive method for routine analyses of the meat storage state.

Extraction of chlorophyll concentration maps from AOTF hyperspectral imagery

Remote mapping of chlorophyll concentration in leaves is highly important for various biological and agricultural applications. Multiple spectral indices calculated from reflectance at specific wavelengths have been introduced for chlorophyll content quantification. Depending on the crop, environmental factors and task, indices differ. To map them and define the most accurate index, a single multi-spectral imaging system with a limited number of spectral channels is insufficient. When the best chlorophyll index for a particular task is unknown, hyperspectral imager able to collect images at any wavelengths and map multiple indices is in need. Due to precise, fast and arbitrary spectral tuning, acousto-optic imagers provide highly optimized data acquisition and processing. In this study, we demonstrate the feasibility to extract the distribution of chlorophyll content from acousto-optic hyperspectral data cubes. We collected spectral images of soybean leaves of 5 cultivars in the range 450–850 nm, calculated 14 different chlorophyll indices, evaluated absolute value of chlorophyll concentration from each of them via linear regression and compared it with the results of well-established spectrophotometric measurements. We calculated parameters of the chlorophyll content estimation models via linear regression of the experimental data and found that index CIRE demonstrates the highest coefficient of determination 0.993 and the lowest chlorophyll content root-mean-square error 0.66 μg/cm2. Using this index and optimized model, we mapped chlorophyll content distributions in all inspected cultivars. This study exhibits high potential of acousto-optic hyperspectral imagery for mapping spectral indices and choosing the optimal ones with respect to specific crop and environmental conditions.

The hybrid approach—convolutional neural networks and expectation maximisation algorithm—for tomographic reconstruction of hyperspectral images

We present a simple, but novel, hybrid approach to hyperspectral data cube reconstruction from computed tomography imaging spectrometry (CTIS) images that sequentially combines neural networks and the iterative expectation maximisation (EM) algorithm. We train and test the ability of the method to reconstruct data cubes of 100 × 100 × 25 and 100 × 100 × 100 voxels, corresponding to 25 and 100 spectral channels, from simulated CTIS images generated by our CTIS simulator. The hybrid approach utilises the inherent strength of the Convolutional Neural Network (CNN) with regards to noise and its ability to yield consistent reconstructions and make use of the EM algorithm’s ability to generalise to spectral images of any object without training. The hybrid approach achieves better performance than both the CNNs and EM alone for seen (included in CNN training) and unseen (excluded from CNN training) cubes for both the 25- and 100-channel cases. For the 25 spectral channels, the improvements from CNN to the hybrid model (CNN + EM) in terms of the mean-squared errors are between 14 % and 26 %. For 100 spectral channels, the improvements between 19 % and 40 % are attained with the largest improvement of 40 % for the unseen data, to which the CNNs are not exposed during the training.