Channel Matrix Research Articles

BER performance analysis of OTFS systems with power allocation

Orthogonal time frequency space (OTFS), as a novel 2-D modulation technique, has been proposed to achieve better BER performances over delay-Doppler channels. In this paper, we propose two different power allocation (PA) algorithms in OTFS systems with zero forcing (ZF) or minimum mean square error (MMSE) equalization, where general formulas with PA are derived in advance under the condition of minimum BER (MBER) criterion. On one hand, a suboptimal MBER power allocation method is put forward to achieve better BER performances, and then analytical BER expressions are derived with proposed PA strategy. Considering the case of MMSE equalization, a combined subsymbol allocation (SA) and PA strategy is raised, where some subsymbols may be abandoned due to worse channel conditions, and then it is proven effectively to improve BER performances through theoretical and simulation results. Furthermore, BER performances with proposed joint SA and PA strategy are also investigated in delay-Doppler channels, where an improved message passing (MP) receiver based on equivalent channel matrix with PA is given.

Methodology positional controlling of communications aerial platform in FANET in the minds of influction of radio electronic countermeasures

FThe article considers the method of controlling the positioning of communication aerial platforms in the FANET network in the conditions of radio-electronic countermeasures to achieve the target function: increasing the accuracy of managing the navigation parameters (movement) of communication aerial platforms (reducing the deviation from the target trajectory). The work shows the process of controlling the parameters of FANET communication aerial platforms positioning in the process of deployment, operation, and control of the rotation process of the main node of the air communication subnet. The deviation of the navigation parameters of the communication aerial platforms was estimated using simulation modeling. The process of determining the coordinates of the communication aerial platforms based on the received signals (probes) on the main transmission channel has been formalized. The article shows the use of a backup channel based on LoRа, to maintain control in conditions of loss of GPS signals, which can become the basis for estimating the energy consumption of the communication aerial platforms network in the process of information exchange. The process of adaptive adjustment of the navigation parameters of the communication aerial platforms is proposed to be carried out using the Kalman filter. The scientific novelty of the method consists in the application of a scientifically methodical apparatus of trigonometric transformations of the channel matrix and calculation of azimuthal and elevation angles for additional correction of navigation parameters by positioning the communication aerial platforms relative to the mobile base station. This approach allows you to achieve optimization of the target functions of the positioning management process and ensure real-time decision-making. The results of simulation modeling confirm the possibility of providing a smaller deviation of navigation parameters up to 30 m compared to the known solution using the PSO algorithm 340–400 m in height.

Non-invasive transcranial volumetric ultrasound localization microscopy of the rat brain with continuous, high volume-rate acquisition

Rationale: Structure and function of the microvasculature provides critical information about disease state, can be used to identify local regions of pathology, and has been shown to be an indicator of response to therapy. Improved methods of assessing the microvasculature with non-invasive imaging modalities such as ultrasound will have an impact in biomedical theranostics. Ultrasound localization microscopy (ULM) is a new technology which allows processing of ultrasound data for visualization of microvasculature at a resolution better than allowed by acoustic diffraction with traditional ultrasound systems. Previous application of this modality in brain imaging has required the use of invasive procedures, such as a craniotomy, skull-thinning, or scalp removal, all of which are not feasible for the purpose of longitudinal studies. Methods: The impact of ultrasound localization microscopy is expanded using a 1024 channel matrix array ultrasonic transducer, four synchronized programmable ultrasound systems with customized high-performance hardware and software, and high-performance GPUs for processing. The potential of the imaging hardware and processing approaches are demonstrated in-vivo. Results: Our unique implementation allows asynchronous acquisition and data transfer for uninterrupted data collection at an ultra-high fixed frame rate. Using these methods, the vasculature was imaged using 100,000 volumes continuously at a volume acquisition rate of 500 volumes per second. With ULM, we achieved a resolution of 31 µm, which is a resolution improvement on conventional ultrasound imaging by nearly a factor of ten, in 3-D. This was accomplished while imaging through the intact skull with no scalp removal, which demonstrates the utility of this method for longitudinal studies. Conclusions: The results demonstrate new capabilities to rapidly image and analyze complex vascular networks in 3-D volume space for structural and functional imaging in disease assessment, targeted therapeutic delivery, monitoring response to therapy, and other theranostic applications.

Channel Bi-Diagonalization for MIMO Communications

This letter proposes a multi-input multi-output (MIMO) transceiver design termed channel bi-diagonalization (CBD), whose precoder and equalizer bi-diagonalize the channel matrix. By representing the bidiagonal MIMO channel with a trellis diagram, we can apply the Viterbi algorithm for the maximum likelihood (ML) detection and decoding, or the BCJR algorithm for the maximum a posteriori (MAP) detection and decoding, which drastically simplifies the optimal MIMO communications. Simulation results verify the superior performance of the proposed CBD scheme.

Modified User Grouping and Hybrid Precoding for Information Decoding and Energy Harvesting in Hardware Impaired Point-To-Point MM-Wave Massive MIMO NOMA

The fifth generation (5G) and beyond 5G race covers both spectral-efficient and energy-efficient mechanisms such as simultaneous wireless information decoding and energy harvesting (SWIDEH). Structured as full or sub-connection of hybrid-precoded mm-wave massive multiple-input multiple-output non-orthogonal multiple access (NOMA) systems. However, the more practical hardware-impaired (HI) functionality yet to be considered for point-to-point (p-to-p) MIMO is conceived from an existing system. A hardware impairment-based power splitting is proposed for energy harvesting. The energy of the HI signal is harnessed through the joint optimization of power allocation (PA) for information decoding (ID) and the power splitting (PS) factor for energy harvesting (EH) using zero-forcing (ZF) precoding and minimum mean square error (MMSE) downlink (DL) detection. Based on the simulation results, an adaptive cluster head selection (CHS) criterion is proposed for analog precoding to mitigate intracluster interferences at a high signal-to-noise ratio (SINR). A successive interference cancellation (SIC) is carried out to enable dynamic channel overhead estimation and user signal detection. An investigation is done by simulating the system performance at varied numbers of users, the number of radio-frequency (RF) chains, and channel characteristics for modelling the user group threshold coupled with channel size reduction via an antenna selection scheme. Observing the execution time and some graphical plots shows that the spectral and energy efficiency can be improved by a random (R) or maximum norm average (MNA) channel vector formation from each user’s channel matrix combined with the best adaptive correlation threshold during CHS and a regularized ZF (RZF) precoder.

Complex matrix and multi-feature collaborative learning for polarimetric SAR image classification

Nearest-regularized subspace (NRS) algorithm is an effective tool to obtain both accuracy and speed for PolSAR image classification. However, existing NRS-based methods can only learn the polarimetric feature vector well, but ignore the PolSAR complex matrix structure and channel correlation. So, how to collaboratively learn the original complex matrix and multiple features to improve the classification accuracy is a key problem. Besides, speckle noises are also the main factor of causing misclassification. To address these limitations, two novel methods are proposed. Firstly, a superpixel-based Riemannian NRS(SRNRS) method is proposed, which can not only learn complex matrix structure by Riemannian metric, but also reduce the speckle noises and computing time by superpixels. Then, a superpixel-based collaborative learning method(CM_SJNRS) is proposed, which integrates the complex matrix and multiple features into the NRS classification framework for the first time. Coupled dictionaries and different metrics are designed for two kinds of feature spaces respectively, and then a collaborative learning model is developed to fuse them. Experimental results demonstrate the proposed SRNRS method can reduce both the speckle and computing time, and the proposed CM_SJNRS method can improve classification performance by fusing two types of features.

Channel estimation for reconfigurable intelligent surface-assisted mmWave based on Re‘nyi entropy function

This study focuses on channel estimation for reconfigurable intelligent surface (RIS)-assisted mmWave systems, in which the RIS is used to facilitate base-to-user data transfer. For beamforming to work with active and passive elements, a large-size cascade channel matrix should always be known. Low training costs are achieved by using the mmWave channels’ inherent sparsity. The research provides a unique compressive sensing-based channel estimation approach for reducing pilot overhead issues to a minimum. The proposed technique estimates channel data signals in a downlink for RIS-assisted mmWave systems. The mmWave systems often have a sparse distribution of signal sources due to the spatial correlations of the domains. This distribution pattern makes it possible to use compressive sensing methods to resolve the channel estimation issue. In order to decrease the pilot overhead, which is necessary to predict the channel, the proposed method extends the Re‘nyi entropy function as the sparsity-promoting regularizer. In contrast to conventional compressive sensing techniques, which necessitate an initial knowledge of the signal’s sparsity level, the presented method employs sparsity adaptive matching pursuit (SAMP) techniques to gradually determine the signal’s sparsity level. Furthermore, it introduces a threshold parameter based on the signal’s energy level to eliminate the sparsity level requirement. Extensive simulations show that the presented channel estimation approach surpasses the traditional OMP-based channel estimation methods in terms of normalized mean square error performance. In addition, the computational cost of channel estimation is lowered. Based on the simulations, our approach can estimate the channel well while reducing training overhead by a large amount.

Joint design of ordered QR precoding and SIC detection for MIMO VLC systems.

Ordered successive interference cancellation (OSIC) detection has been investigated to mitigate the high spatial correlation for multiple-input multiple-output (MIMO) visible light communication (VLC) systems. However, existing OSIC schemes have to perform reordering and matrix inversion for each detected symbol, which may lead to high complexity when a large number of symbols are transmitted. In this work, a joint design of ordered QR decomposition precoding and SIC detection (OQR-SIC) is proposed for MIMO VLC systems. This work jointly investigates OQR precoding and SIC detection to reduce the detection complexity while alleviating spatial correlation issue for MIMO VLC systems. In OQR-SIC, with the upper triangular matrix obtained by QR decomposition, the SIC detector can detect the symbol sequentially without reordering and matrix inversion calculations. To improve the system data rate, we further optimize the ordering of the columns of the channel matrix before QR decomposition and the power allocation of transmitted signals under the constraints of dimming control, total electrical power and reliable SIC detection. Simulation results demonstrate that the proposed OQR-SIC achieves 2 dB and 9.8 dB signal-to-noise ratio gains compared to conventional QR-SIC in 4 × 4 and 9 × 9 MIMO VLC systems, respectively, when the bit error rate is 10-3.

Breakthroughs on tailoring membrane materials for ethanol recovery by pervaporation

• Mixed matrix membranes (MMMs) with well-designed membrane structures may provide both high permeability and membrane selectivity to break trade-off effect due to the better control over physi-/chemical micro-environment and cavity/pore size as well as size distribution. • Fillers should be orderly arranged in polymer matrix and form continuous transport channels for ethanol to full play the synergistic effect of polymer and fillers. • Building firm bonding interactions between filler and polymer is one of the most promising methods to strengthen the PV performance of MMMs. • The development of bioinspired materials and structures provides enlightening ideas for the construction of ethanol perm-selective membranes. Bioethanol, as a clean and renewable fuel, has gained increasing attention due to its major environmental benefits. Pervaporation (PV) is a promising and competitive technique for the recovery of ethanol from bioethanol fermentation systems due to the advantages of environmental friendliness, low energy consumption and easy coupling with fermentation process. The main challenge for the industrial application of ethanol perm-selective membranes is to break the trade-off effect between permeability and selectivity. As membrane is the heart of the pervaporation separation process, this article attempts to provide a comprehensive survey on the breakthroughs of ethanol perm-selective PV membranes from the perspectives of tailoring membrane materials to enhance PV separation performance. The research and development of polymeric and organic/inorganic hybrid membranes are reviewed to explore the fundamental structure-property-performance relationships. It is found that mixed matrix membranes with well-designed membrane structures offer the hope of better control overphysi-/chemical micro-environment and cavity/pore size as well as size distribution, which may provide both high permeability and membrane selectivity to break the trade-off effect. The tentative perspective on the possible future directions of ethanol perm-selective membranes is also briefly discussed, which may provide some insights in developing a new generation of high-performance PV membranes for ethanol recovery.

Spectral Efficiency of OTFS Based Orthogonal Multiple Access With Rectangular Pulses

In this paper, we consider Orthogonal Time Frequency Space (OTFS) modulation based multiple-access (MA). We specifically consider Orthogonal MA methods (OMA) where the user terminals (UTs) are allocated non-overlapping physical resource in the delay-Doppler (DD) and/or time-frequency (TF) domain. Well known OMA methods include, i) Guard Band (GB) based MA (GBMA), ii) Interleaved Delay Doppler MA (IDDMA), iii) Interleaved Time Frequency MA (ITFMA). The spectral efficiency (SE) performance of these OMA methods has <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">only</i> been studied for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ideal</i> transmit and receive pulses. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">With ideal pulses</i> , IDDMA and ITFMA are free from multi-user interference (MUI) and unlike GBMA they <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">do not</i> use guard bands in the DD/TF domain. Since ideal pulses are not realizable, in this paper we study the SE performance of these OMA methods with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">practical rectangular pulses</i> . For these OMA methods, we derive the expression for the received DD/TF domain symbols at the base station (BS) receiver and the effective DD domain channel matrix when rectangular pulses are used. Study of these expressions reveals the presence of MUI when rectangular pulses are used, although the amount of MUI in IDDMA is observed to be significantly smaller than that in ITFMA. We also derive the expression for the achievable sum SE. Through simulations, for practical values of the received signal-to-noise ratio, we observe that with rectangular pulses the sum SE achieved by the IDDMA method is significantly higher than that achieved by the ITFMA and GBMA methods.

Orthogonal Delay-Doppler Division Multiplexing Modulation

Inspired by the orthogonal time frequency space (OTFS) modulation, in this paper, we consider designing a multicarrier (MC) modulation on delay-Doppler (DD) plane, to couple the modulated signal with a doubly-selective channel having DD resolutions. A key challenge for the design of DD plane MC modulation is to investigate whether a realizable pulse orthogonal with respect to the DD plane’s fine resolutions exists or not. To this end, we first indicate that a feasible DD plane MC modulation is essentially a type of staggered multitone modulation. Then, analogous to orthogonal frequency division multiplexing, we propose an orthogonal delay-Doppler division multiplexing (ODDM) modulation, and design the corresponding transmit pulse. Furthermore, we prove that the proposed transmit pulse is orthogonal with respect to the DD plane’s resolutions and therefore a realizable DD plane orthogonal pulse does exist. The orthogonality of this particular pulse significantly eases the derivation of the ODDM’s DD domain channel input-output relation, and yields a channel matrix with an elegant block-circulant-like structure. We demonstrate that the ODDM outperforms the OTFS in terms of out-of-band emission and bit error rate, by achieving perfect coupling between the modulated signal and the DD channel.

A Joint Equalization and Decoding Technique for Multiuser Massive MIMO Uplink System With Transmitter and Receiver RF Impairments Under Doubly Selective Channels

The impairments due to in-phase and quadrature-phase imbalance at the transmitter and/or receiver, carrier frequency offset, and doubly selective channel (DSC) result in multiuser interference (MUI) and self-intercarrier interference (S-ICI) in multiuser massive multiple-input–multiple-output (MIMO) uplink systems. The MUI and S-ICI significantly deteriorate the performance of the receiver and make data detection quite a challenging task. To tackle this issue, we developed a novel crisscross banded effective channel matrix and a joint equalization and detection technique for multiuser massive MIMO single-carrier frequency division multiple access/orthogonal frequency division multiple access uplink systems with RF impairments under DSC. During each iteration of the proposed method, the MUI and S-ICI are calculated using the soft information from the decoder section, and then the interference canceled signal is fed back to the equalizer section for the joint equalization of the mirror subcarrier pairs. Since the proposed method does not put any restriction on the allocation of mirror subcarrier pairs, it is equally applicable to all types of carrier assignment schemes. Further, the extrinsic information transfer chart of the proposed technique is developed for analyzing the convergence. Extensive simulation studies are conducted to validate the performance of the proposed technique.

Wideband mmWave MIMO: One Prior-Aided LAMP-Based Network Combining with Residual Learning for Beamspace Channel Estimation

Existing channel estimation schemes for wideband systems generally estimate the channel matrix by pre-estimating the common support, which has a limited validity owing to the effect of beam squint. It is worth noting that the learned approximate message passing (LAMP) network need not pre-estimate the support and has obtained a relatively reliable estimation quality in the narrowband systems. In order to degrade the performance penalty caused by inaccurate estimation of the support in the wideband millimeter-wave MIMO systems, a prior-aided Gaussian mixture LAMP (GM-LAMP) network combining with residual learning is presented. Specifically, the multicarrier Gaussian mixture threshold shrinkage function is constructed for the GM-LAMP network, which can directly estimate the wideband beamspace channel while avoiding pre-estimating the support; then, considering the impact of channel noise and the coarse estimation error by the GM-LAMP, a residual network (ResNet) is designed to improve the estimation performance. Simulation results validate the efficiency of the proposed network (referred to as GLAMP-ResNet) with the lower computational complexity compared with the existing schemes.

A Next-Generation Codebook Evolution Strategy for Massive Arrays Using Deep Neurals Networks

The discrete Fourier transform (DFT)-based codebook is currently among the mostly commonly adopted codebooks for beamforming using arrays of different shapes and sizes, including the large-scale two-dimensional uniform planar array (UPA). DFT-based codevectors can be easily generated in arbitrary angle resolutions and apply well to millimeter-wave (mmWave) channels due to their directive nature of resulting beams. However, a fixed set of codevectors is applied regardless of the user distributions and the propagation environment, which may exhibit limited beamforming performance under certain transmission scenarios. In this paper, we propose a new way of generating a set of beamforming vectors for multiple-input multiple-output (MIMO) transmission using massive arrays under the limited feedback of the channel state information (CSI). Precoder matrix indicator (PMI) and channel quality indicator (CQI) reports from the users have become the sources for the generation of a new set of codevectors, which are autonomously determined by the deep learning (DL) module at the base station (BS). The process is operated in an iterative fashion to produce updated versions of the codebook with the reduced return of the loss function at the deep neural network (DNN). The time-varying codebook for each BS automatically reflects the characteristics of a given wireless environment to adapt to its channel and traffic conditions. The reference signal (RS) at the BS is periodically transmitted in the form of beamformed CSI-RS, thus the operation is transparent to the users of the system and no significant specification changes are necessary. A simple plug-and-play type of BS installation suffices to achieve the potential gain of the proposal, which is demonstrated by the implementation details of the DL engine and the corresponding performance simulation results.

A UAV-Swarm-Communication Model Using a Machine-Learning Approach for Search-and-Rescue Applications

This paper presents a UAV-swarm-communication model using a machine-learning approach for search-and-rescue applications. Firstly, regarding the communication of UAVs, the receive signal strength (RSS) and power loss have been modeled using random forest regression, and the mathematical representation of the channel matrix has also been discussed. The second part consisted of swarm control modeling of UAVs; however, a dataset for five types of triangular swarm formations was generated, and K-means clustering was applied to predict the cluster. In order to obtain the correct swarm formation, the dendrogram of all types was investigated. Finally, the heat map and contour were plotted for all kinds of swarm clusters. Furthermore, it was observed that the RSS of proposed swarms had good agreement with swarm distances.

Parallel minimum mean square error equalization for reduced‐zero‐padding orthogonal time frequency space with the aid of unitary precoding

AbstractThis work studies the equalization method for the reduced‐prefix version of the orthogonal time frequency space (OTFS) modulation in which one zero‐padding (ZP) is inserted in each frame. We focus on applications in low data rate scenarios such as the Internet of Things, and will consider the case where the number of subcarriers and time slots are small. The idea of this work is to retain the large singular values of the channel matrix through linear transformations, while discarding the remaining small singular values. This makes it possible to avoid performance degradation due to small singular values when inverting the matrix in the minimum mean square error (MMSE) equalization. Specifically, a joint unitary precoding and signal linear transformation method is proposed for the reduced‐ZP OTFS modulation which decomposes the whole system into parallel subsystems. Then, the receiver can perform parallel MMSE equalization, where the singular values of each branch are not small. Simulation results show that the proposed method can achieve better bit error rate performance than the state‐of‐the‐art methods like message passing, unitary approximate message passing, and variational unitary approximate message passing.

High-Temperature Creep Behavior of a Nickel-Based Single-Crystal Superalloy with Small-Angle Deviation from [111] Orientation

By means of tensile creep tests and microstructure analysis, the creep behavior and deformation mechanism of a nickel-based single-crystal alloy with small-angle deviations from the [111] orientation at 1040°C/137 MPa were investigated. The results suggested that in the early stage of creep, proliferating dislocations generated by different slip systems get accumulated in the γ phase. Dislocations mainly slipped in the γ phase and climbed over the γ′ phase, and they began to form a dislocation network at the interface. γ′ phases were connected to each other, and the coherence relationship was destroyed. In the steady-state stage of creep, the solid interfacial dislocation network was formed, and the γ′ phase transformed into a lamellar raft structure, which hinders the slip and climb of dislocations in the matrix channel. In the accelerated creep stage, the dislocation network was destroyed, and dislocations sheared into the γ′ phase in the way of dislocation pairs, which could react to form a superdislocation node and decompose to form APBs on the &lt;111&gt; plane or cross slip from the &lt;111&gt; plane to the &lt;100&gt; plane to form K-W locks.

Symbol detection using extreme learning machine network for MU‐SIMO systems

This paper focuses on symbol detection for a multi-user single-input multiple-output (MU-SIMO) uplink using supervised machine learning techniques. An extreme learning machine (ELM) is chosen as the equalizer at the receiver end due to its super-fast learning ability and minimum training error. To tune the parameters, a pilot based online training for an ELM network is proposed, and those parameters are further used to detect the unknown transmitted symbols. Conventionally, the channel matrix is estimated using known pilot symbols explicitly and then the transmitted symbol is recovered using a linear equalizer. Here, instead of directly estimating the channel coefficients, the symbols are detected using an ELM based direct equalizer followed by a hard decision rule. To reduce the pilot requirement of the proposed model, a method is discussed where the channel is estimated using a small number of pilot symbols and the ELM network is trained using a separate training dataset along with the channel estimate. Furthermore, the performance comparison between the proposed ELM based equalizers, linear equalizers, and nonlinear detection techniques is shown.

Investigation on the influence of Ta on the microstructure evolution of Ni-based superalloy DZ411 during directional solidification, heat treatment, and long-term aging

The microstructure evolution in directionally solidified Ni-based superalloys DZ411 with different Tantalum (Ta) contents (2.72, 3.10, and 4.00 wt%) was investigated. After directional solidification, three alloys with different Ta contents were subjected to standard heat treatment: solution treatment (1230 °C/2 h/AC)+ primary aging (1120 °C/2 h/AC)+ secondary aging (870 °C/24 h/AC). Then, following isothermal long-term aging treatments were performed at 950 °C for 50, 100, 200, 500 and 1000 h. The addition of Ta can lead to the increase of the volume fractions of MC carbides, eutectics, and γ′ phases during directional solidification. In addition, with the increase of Ta content, the mismatch of γ/γ′ increases, thus, the shape of γ′ becomes more regular. After solution heat treatment, the MC carbides are decomposed, and more M23C6 carbides are precipitated along the grain boundaries in alloys with increasing Ta contents. Besides, the eutectic cannot be completely eliminated. After secondary aging, more secondary γ′ phases are precipitated on the γ matrix channels in alloys with increasing Ta contents. Furthermore, the addition of Ta can delay the coalescence of the γ′ phase during long-term aging, which can be attributed to the reduction of the coarsening rate K according to the precipitation coarsening theory of Lifshitz and Slyozov and Wanger (LSW).

ERA: A new, fast, machine learning-based software to document rock paintings

The present study proposes a new software program to help researchers identify rock paintings from digital images, rapidly producing high-quality documentation, in a user-friendly way. The three RGB colour channels of the digital image are first decorrelated and then stretched, a well-known technique used by remote-sensing specialists for over thirty years. In contrast with the approaches previously developed specifically for rock art, several data-whitening algorithms are used at this step: (regular) principal component analysis, zero-phase component analysis, Cholesky decomposition, and independent component analysis. These transformations produce different arrangements of the colour information, which nevertheless share some important properties (e.g. the covariance matrix of the new channels equals the identity matrix). The decorrelated data, previously stretched and scaled to fit the RGB space, are then converted into various colour spaces (selected from among the most popular): XYZ, HLS, HSV, LAB (CIELAB), Luv, CMY(K), YCrCb, and YUV. The most subtle colour variations will be better perceived in some of these newly produced, contrasted, false-coloured images. The researcher can then take advantage of supervised machine learning algorithms to isolate painted figures. At this step, binary pixel classification is performed either by logistic regression, support vector machine, or k -nearest neighbours, possibly including confident learning. There is no need for complex tuning at any point during the procedure, which lasts a few minutes at most, while a posteriori cleaning of the produced document is minimal. The software, written in Python, is provided as a stand-alone executable program for Windows, for broader diffusion, and as open-source code, which can therefore be adapted to the evolving needs of the community.