Matrix Size Research Articles

SPICE-Compatible Circuit Models of Multiports Described by Scattering Parameters with Arbitrary Reference Impedances

New SPICE-compatible circuit models of a multiport are presented here that are suitable for the frequency-domain and time-domain analyses of hybrid systems containing linear distributed elements and possibly non-linear lumped elements. Distributed elements models are based on scattering parameters with potentially complex reference impedances, which are not necessarily equal for all ports. Both exact and approximated (lumped) models are proposed. The scattering parameters are directly taken as the model element values in the former case. In the latter case, the model element values are equal to the real and imaginary parts of the poles and residues of the rational approximation. The models comprise a multiport (with an admittance matrix numerically equal to the modeled scattering matrix or approximating it) equipped with a pair of coupled impedances at each port. A few examples validate the proposed approach and prove its efficiency in terms of matrix size and analysis time compared to some selected commercial counterparts.

CT angiography of the lower limbs: combining small field of view with large matrix size and iterative reconstruction further improves image quality of below-the-knee arteries.

Image quality and diagnostic accuracy in computed tomography angiography (CTA) reach their limits in imaging of below-the-knee vessels. To evaluate whether image quality in CTA of lower limbs is further improvable by combining side-separate reconstruction with a larger matrix size and whether resulting noise can be compromised with iterative reconstruction (IR). From CTA of the lower extremities of 26 patients (5 women, 21 men; mean age = 68.5 ± 10.3 years), the lower legs were reconstructed side-separately with different reconstruction algorithms and matrix sizes including filtered back projection (FBP) with a 512 × 512 matrix, FBP with a 1024 × 1024 matrix, IR (SAFIRE) with a 512 × 512 matrix, and IR (SAFIRE) with a 1024 × 1024 matrix. A total of 208 CT series were evaluated. Subjective image quality was assessed by two readers using a 5-point Likert scale. Image noise was assessed by measuring signal-to-noise and contrast-to-noise ratios. Subjective image quality was rated significantly higher when using a 1024 × 1024 matrix (P < 0.001) and could further be increased with IR. Vessel sharpness was rated significantly better with a larger matrix (P < 0.001). Visible and measured image noise was significantly higher with a 1024 × 1024 matrix but could be reduced by using IR (P < 0.001), even to a level below FBP with a 512 × 512 matrix while reconstructing with a larger matrix (P < 0.001). Image quality, image noise, and vessel sharpness can be further improved in CTA of the lower extremities with side-separate reconstruction using a 1024 × 1024 matrix size and IR.

L1-gain control for 2D delayed positive continuous Markov jumping systems

This study is focused on analyzing the L1-stochastic internal stability and the design of an L1-gain controller for two-dimensional (2D) continuous positive Markov jumping systems (PMJSs) with constraints on the inputs and states. An algorithm is developed to explicitly determine the state feedback control law with the optional L1-gain performance. First, by constructing a co-positive stochastic Lyapunov function for the positive system and establishing the equation for the Markov states' mathematical expectation, several sufficient and necessary conditions for L1-stochastic internal stability are derived. This analysis indicates that 2D PMJSs with directional delays are influenced by sizes of the system matrices and magnitude of delays, and transition matrix. Second, a method for calculating the L1-gain is formulated utilizing linear programming (LP), thus, an L1-gain controller is designed to guarantee that the closed-loop system is positive and L1-stochastically internally stable, while achieving optimal L1-gain performance. Two numerical and practical examples are considered, and the influence of delays and transition probability matrices on the L1-gain is specified to validate the preceding theoretical findings.

Continuous Time Algebraic Riccati Equation Solution for Second Order Systems

Abstract The continuous time algebraic Riccati equation (ARE) is often utilized in control, estimation, and optimization. For a linear system with a second order structure, the ARE required to be solved to get the control values in standard control problems results in complex sub-equations in terms of the second order system matrices. The computational costs of solving the algebraic Riccati equation through standard methods such as the Hamiltonian matrix pencil approach increase substantially as matrix sizes increase for a second order system, due to the eigendecomposition of the 2n x 2n system matrices involved. This work introduces a new solution that does not require the eigendecomposition of the 2n x 2n system matrices, while satisfying all of the requirements of the solution to the Riccati equation (e.g., detectability, stabilizability, positive semi-definite solution matrix).

Synthetic orbit uncertainty generation through regression analysis of historical Conjunction Data Messages

In the last decades, the Earth-orbiting population of both active and non-active objects has grown significantly, leading to a substantial increase in number of possible in-orbit collisions. It is therefore crucial to monitor the orbit of space resident objects to assess in advance the threat of risky conjunctions. Within this framework, the 18th Space Defense Squadron (SDS) is consistently updating the orbit of thousands of tracked objects by processing observations of the U.S. Space Surveillance Network (SSN). The determined orbital data is continuously maintained in the Special Perturbation (SP) catalogue and used by the 19th SDS to issue close approach warnings to satellite operators around the globe in the form of Conjunction Data Messages (CDM). The Flight Dynamics (FD) group of the German Space Operation Centre (GSOC) receives on regular basis a subset of the SP catalogue data along with CDMs associated to the fleet of its controlled satellites. The SP ephemerides are in fact provided without any covariance information preventing any computation of the Probability of Collision (Pc). In GSOC FD we are implementing a service to link a series of synthetic orbital error covariance matrices to a given SP ephemeris by statistically analyzing historical CDMs of past events. More than 30 GB of past conjunction data are processed to extract state vector, covariance matrix and object size parameter of already encountered secondary objects. The orbital errors of these last are subsequently categorized and divided into orbital classes to decouple the high correlation the covariance has with respect to solar flux, object dimension, altitude of perigee, eccentricity and orbit inclination. The classification aims at collecting similar CDMs regarding the aforementioned dependencies, and approximates the predicted 1-sigma position errors in the orbital frame by optimal curve-fitting techniques. By evaluation of the curve fitting coefficients of a requested orbit class a covariance matrix can be generated for any prediction time in upcoming CDM refinements and other analyses. The work discusses the limiting cases of the classification approach, bringing possible solutions to the scenario of empty classes. An in-depth characterization of the parameters that affect the orbital errors is in fact performed to individualize the neighboring class that provides the closest and most meaningful covariance timeline. Successively, the effect of using synthetic covariance in a conjunction risk assessment is also explored, adapting the problem on real operations. Lastly, the entire data processing pipeline and how the described service fits into the GSOC Flight Dynamics System (FDS) framework is described.

Approximate Analytical Solution of the Ground State Problem of He and He-like Ions using Symmetrized-Hydrogenic States

The matrix method using three symmetrized-hydrogenic basis states has been applied to analytically obtain an approximate solution to the Schrödinger equation of the Helium atom and some He-like ions (2&lt;Z&lt;10). This study aims at obtaining more accurate ground state energies of the systems compared to our previous calculation using un-symmetrized basis states and some other simple calculations in the literature. The contribution of the symmetrized basis states on the ground state energies of the systems is also investigated. The time-independent Schrödinger equation involving a 3×3 Hamiltonian matrix, formed by hydrogenic s-states, was analytically solved to obtain three energy eigenvalues of the systems as well as their corresponding eigenvectors. Results showed that the 1s2 energies of the systems were more accurate than our previous unsymmetrized basis calculations, with significant error reduction observed for He and Li+. With the same matrix size, the ground state energies of He and He-like ions obtained from three symmetrized basis states in this study were found to be closer to the exact and experimental energies than those obtained from unsymmetrized basis states. It was also demonstrated that the |100;100&gt; state made the largest contribution to the ground state energies of the systems, i.e. about 90.9% for He and around 99.9% for Ne8+, and consequently the smallest contribution came from the other two symmetrized states (less than 1%). To conclude, the calculated ground state energies were more accurate than some other simple calculations reported in the literature.

An efficient full-size convolutional computing method based on memristor crossbar

Modern artificial intelligence systems based on neural networks need to perform a large number of repeated parallel operations quickly. Without hardware acceleration, they cannot achieve effectiveness and availability. Memristor-based neuromorphic computing systems are one of the promising hardware acceleration strategies. In this paper, we propose a full-size convolution algorithm (FSCA) for the memristor crossbar, which can store both the input matrix and the convolution kernel and map the convolution kernel to the entire input matrix in a full parallel method during the computation. This method dramatically increases the convolutional kernel computations in a single operation, and the number of operations no longer increases with the input matrix size. Then a bidirectional pulse control switch integrated with two extra memristors into CMOS devices is designed to effectively suppress the leakage current problem in the row and column directions of the existing memristor crossbar. The spice circuit simulation system is built to verify that the design convolutional computation algorithm can extract the feature map of the entire input matrix after only a few operations in the memristor crossbar-based computational circuit. System-level simulations based on the MNIST classification task verify that the designed algorithm and circuit can effectively implement Gabor filtering, allowing the multilayer neural network to improve the classification task recognition accuracy to 98.25% with a 26.2% reduction in network parameters. In comparison, the network can even effectively immunize various non-idealities of the memristive synaptic within 30%.

Joint Robust Variable Selection of Mean and Covariance Model via Shrinkage Methods

SummaryA valuable and robust extension of the traditional joint mean and the covariance models when data subject to outliers and/or heavy‐tailed outcomes can be achieved using the joint modelling of location and scatter matrix of the multivariate t‐distribution. This model encompasses three models in itself, and the number of unknown parameters in the covariance model increases quadratically with the matrix size. As a result, selecting the important variables becomes a crucial aspect to consider. In this context, the variable selection combined with the parameter estimation is considered under the normality assumption. However, because of the non‐robustness of the normal distribution, the resulting estimators will be sensitive to outliers and/or heavy taildness in the data. This paper has two objectives to overcome these problems. The first is to obtain the maximum likelihood estimates of the parameters and propose an expectation‐maximisation type algorithm as an alternative to the Fisher scoring algorithm in the literature. We also consider simultaneous parameter estimation and variable selection in the multivariate t‐joint location and scatter matrix models. The consistency and oracle properties of the regularised estimators are also established. Simulation studies and real data analysis are provided to assess the performance of the proposed methods.

Solutions to the Landau–Lifshitz–Gilbert equation in the frequency space: Discretization schemes for the dynamic-matrix approach

The dynamic matrix method addresses the Landau–Lifshitz–Gilbert (LLG) equation in the frequency domain by transforming it into an eigenproblem. Subsequent numerical solutions are derived from the eigenvalues and eigenvectors of the dynamic matrix. In this work we explore discretization methods needed to obtain a matrix representation of the dynamic operator, a fundamental counterpart of the dynamic matrix. Our approach opens a new set of linear algebra tools for the dynamic matrix method and expose the approximations and limitations intrinsic to it. Moreover, our discretization algorithms can be applied to various discretization schemes, extending beyond micromagnetism problems. We present some application examples, including a technique to obtain the dynamic matrix directly from the magnetic free energy function of an ensemble of macrospins, and an algorithmic method to calculate numerical micromagnetic kernels, including plane wave kernels. We also show how to exploit symmetries and reduce the numerical size of micromagnetic dynamic-matrix problems by a change of basis. This procedure significantly reduces the size of the dynamic matrix by several orders of magnitude while maintaining high numerical precision. Additionally, we calculate analytical approximations for the dispersion relations in magnonic crystals. This work contributes to the understanding of the current magnetization dynamics methods, and could help the development and formulations of novel analytical and numerical methods for solving the LLG equation within the frequency domain.

Critical pressure (Pc) and critical temperature (Tc) of Midra shale

The critical pressure (Pc) and critical temperature (Tc) of shale gas depend on the characteristic pore size because of the importance of fluid–rock interactions in the matrix. This size dependency is neglected in highly permeable formations, where gas composition is only implemented because the fluid–fluid interactions are dominant. This study determines the critical properties by accounting for the characteristic pore size in the shale matrix and gas composition. The analyzed components are carbon dioxide, ethane, methane, n-butane, nitrogen, pentane, and propane. It shows that the bulk properties overestimate the actual critical properties. The overestimation varies between 15 and 26% in a uniform 5 nm conduit with a circular cross section, and it increases nonlinearly when decreasing the conduit size. Overestimation versus size is presented to provide a convenient tool for correcting the existing data. This study also determines the critical properties of Midra shale by accounting for the pore-throat size and pore-body size distributions. The former distribution is based on the mercury injection capillary pressure measurements of eight samples, whereas the latter is based on the nitrogen adsorption measurements of six samples. This study indicates that common bulk properties overestimate the critical properties of the studied shale between 5 and 22%. The results have applications in characterizing multiphase transport in shale gas reservoirs.

Prediction of effect of fabrication parameters on the properties of B4C ceramic particle reinforced AA2024 matrix nanocomposites using neural networks

In the present study, a prediction model was created to predict the impact of B4C content, milling time and matrix size on the hardness and density of AA2024-B4C nanocomposites produced by means of flake powder metallurgy. The process involved synthesizing AA2024-B4C nanocomposite powders by mechanical milling followed by preparing nanocomposites by hot pressing. The matrix size of the AA2024 alloy powders, the milling time, and the B4C content were selected as the input parameters. On the other hand, the density and the hardness of the AA2024-B4C nanocomposites were designed as the output parameters. The results showed that the sintered density is significantly improved by decreasing matrix size. It was found that density of AA2024–3 wt%B4C nanocomposites is lower than AA2024–1 wt%B4C nanocomposites. However, the hardness of AA2024–3 wt%B4C nanocomposites is better than AA2024–1 wt%B4C nanocomposites. The AA2024-B4C nanocomposite prediction model could predict hardness and density with a mean absolute percentage error (MAPE) of 0.32% and 1.38%. The results show that the ANN model is a useful tool for the matrix size effect prediction, milling time and B4C content on the density and hardness of AA2024-B4C nanocomposites prepared by flake powder metallurgy.

Analysis of arsenic-modulated expression of hypothalamic estrogen receptor, thyroid receptor, and peroxisome proliferator-activated receptor gamma mRNA and simultaneous mitochondrial morphology and respiration rates in the mouse.

Arsenic has been identified as an environmental toxicant acting through various mechanisms, including the disruption of endocrine pathways. The present study assessed the ability of a single intraperitoneal injection of arsenic, to modify the mRNA expression levels of estrogen- and thyroid hormone receptors (ERα,β; TRα,β) and peroxisome proliferator-activated receptor gamma (PPARγ) in hypothalamic tissue homogenates of prepubertal mice in vivo. Mitochondrial respiration (MRR) was also measured, and the corresponding mitochondrial ultrastructure was analyzed. Results show that ERα,β, and TRα expression was significantly increased by arsenic, in all concentrations examined. In contrast, TRβ and PPARγ remained unaffected after arsenic injection. Arsenic-induced dose-dependent changes in state 4 mitochondrial respiration (St4). Mitochondrial morphology was affected by arsenic in that the 5 mg dose increased the size but decreased the number of mitochondria in agouti-related protein- (AgRP), while increasing the size without affecting the number of mitochondria in pro-opiomelanocortin (POMC) neurons. Arsenic also increased the size of the mitochondrial matrix per host mitochondrion. Complex analysis of dose-dependent response patterns between receptor mRNA, mitochondrial morphology, and mitochondrial respiration in the neuroendocrine hypothalamus suggests that instant arsenic effects on receptor mRNAs may not be directly reflected in St3-4 values, however, mitochondrial dynamics is affected, which predicts more pronounced effects in hypothalamus-regulated homeostatic processes after long-term arsenic exposure.

Adaptive Speech Coding Method Based on Singular Value Decomposition and Grey Wolf Optimization for Arabic Language

Speech coding plays a crucial role in maintaining speech quality while optimizing network resources and expediting transmission, as well as facilitating the storage of speech data. In this paper, an adaptive method for speech coding using singular value decomposition (SVD), grey wolf optimization (GWO), and run-length encoding (RLE) was proposed. The proposed method streamlines the speech matrix through preprocessing, converting it into short intervals. Subsequently, each interval undergoes decomposition using SVD, followed by optimization of compression quality using GWO. Finally, RLE is employed as the last step to increase space-saving. The developed method was conducted on two datasets: Quran and LibriSpeech using PSNR, PSEQ, and MOS tests. The results demonstrate promising outcomes, achieving space-saving up to 89.80, 84.04, 74.76, 67.24, and 59.52, respectively, for different values of quality (10, 20, 30, 40, and 50). GWO was used to optimize the quality factor which varies in each block, further increasing the space-saving up to 85.77. The average value of PSNR was equal to 21.3, MOS = 4.71, and PSEQ was equal to 3.95. Lastly, the RLE method effectively reduced the size of speech matrices, yielding a highly satisfactory space saving of up to 90.77, while maintaining excellent speech quality.

Exploring the effects of weighting against homoplasy in genealogies of palaeontological phylogenetic matrices.

Although simulations have shown that implied weighting (IW) outperforms equal weighting (EW) in phylogenetic parsimony analyses, weighting against homoplasy lacks extensive usage in palaeontology. Iterative modifications of several phylogenetic matrices in the last decades resulted in extensive genealogies of datasets that allow the evaluation of differences in the stability of results for alternative character weighting methods directly on empirical data. Each generation was compared against the most recent generation in each genealogy because it is assumed that it is the most comprehensive (higher sampling), revised (fewer misscorings) and complete (lower amount of missing data) matrix of the genealogy. The analyses were conducted on six different genealogies under EW and IW and extended implied weighting (EIW) with a range of concavity constant values (k) between 3 and 30. Pairwise comparisons between trees were conducted using Robinson-Foulds distances normalized by the total number of groups, distortion coefficient, subtree pruning and regrafting moves, and the proportional sum of group dissimilarities. The results consistently show that IW and EIW produce results more similar to those of the last dataset than EW in the vast majority of genealogies and for all comparative measures. This is significant because almost all of these matrices were originally analysed only under EW. Implied weighting and EIW do not outperform each other unambiguously. Euclidean distances based on a principal components analysis of the comparative measures show that different ranges of k-values retrieve the most similar results to the last generation in different genealogies. There is a significant positive linear correlation between the optimal k-values and the number of terminals of the last generations. This could be employed to inform about the range of k-values to be used in phylogenetic analyses based on matrix size but with the caveat that this emergent relationship still relies on a low sample size of genealogies.

Effect of difference in microstructure of rare refractory metal silicate doping matrix on oxidation behavior and mechanism of C/SiC composites

Doping refractory metal silicates into the matrix of C/SiC composites is an effective means to improve their oxidation resistance. Previous studies have demonstrated that doping HfSiO4 matrix availably enhanced the oxidation resistance of C/SiC composites, but the high raw material cost of HfSiO4 limits its widespread application. This paper attempts to introduce ZrSiO4 matrix, which has lower raw material cost and similar properties to HfSiO4, into C/SiC matrix through the same process. To clarify whether the microstructure of the refractory metal silicate doped matrix significantly impacts the oxidation behavior of C/SiC composites, the preparation temperature of ZrSiO4 was increased to 1100 °C. The densification effect, oxidation behavior, and related mechanisms of C/SiC composites doped with ZrSiO4 matrix were investigated and compared in detail with the previously studied C/SiC composites doped with HfSiO4 matrix. Results show that the oxidation resistance behavior of C/SiC composites is relatively sensitive to the microstructure of the refractory metal silicate-doped matrix. At lower preparation temperatures of refractory metal silicates, the particle size of the composite matrix is significantly refined, which is conducive to improving the matrix densification degree of the composites and protecting more carbon fibers from erosion by the oxidizing environment, thus achieving a better oxidation resistance modification effect.

Robustness and classification capabilities of MRI radiomic features in identifying carotid plaque vulnerability.

To assess how radiomic features may be combined with plaque morphological and compositional features identified by multi-contrast MRI to improve upon conventional risk assessment models in determining culprit carotid artery lesions. Fifty-five patients (mean age: 62.6; 35 males) with bilateral carotid stenosis who experienced transient ischaemic attack (TIA) or stroke were included from the CARE-II multi-centre carotid imaging trial (ClinicalTrials.gov Identifier: NCT02017756). They underwent MRI within 2 weeks of the event. Classification capability in distinguishing culprit lesions was assessed by machine learning. Repeatability and reproducibility of the results were investigated by assessing the robustness of the radiomic features. Radiomics combined with a relatively conventional plaque morphological and compositional metric-based model provided incremental value over a conventional model alone (area under curve [AUC], 0.819 ± 0.002 vs 0.689 ± 0.019, respectively, P = .014). The radiomic model alone also provided value over the conventional model (AUC, 0.805 ± 0.003 vs 0.689 ± 0.019, respectively, P = .031). T2-weighted imaging-based radiomic features had consistently higher robustness and classification capabilities compared with T1-weighted images. Higher-dimensional radiomic features outperformed first-order features. Grey Level Co-occurrence Matrix, Grey Level Dependence Matrix, and Grey Level Size Zone Matrix sub-types were particularly useful in identifying textures which could detect vulnerable lesions. The combination of MRI-based radiomic features and lesion morphological and compositional parameters provided added value to the reference-standard risk assessment for carotid atherosclerosis. This may improve future risk stratification for individuals at risk of major adverse ischaemic cerebrovascular events. The clinical relevance of this work is that it addresses the need for a more comprehensive method of risk assessment for patients at risk of ischaemic stroke, beyond conventional stenosis measurement. This paper shows that in the case of carotid stroke, high-dimensional radiomics features can improve classification capabilities compared with stenosis measurement alone.

Highly Fault-Tolerant Systolic-Array-Based Matrix Multiplication

Matrix multiplication plays a crucial role in various engineering and scientific applications. Cannon’s algorithm, executed within two-dimensional systolic arrays, significantly enhances computational efficiency through parallel processing. However, as the matrix size increases, reliability issues become more prominent. Although the previous work has proposed a fault-tolerant mechanism, it is only suitable for scenarios with a limited number of faulty processing elements (PEs). This paper introduces a pair-matching mechanism, assigning a fault-free PE as a proxy for each faulty PE to execute its tasks. Our fault-tolerant mechanism comprises two stages: in the first stage, each fault-free PE completes its designated computations; in the second stage, computations intended for each faulty PE are executed by its assigned fault-free PE proxy. The experimental results demonstrate that compared to the previous work, our approach not only significantly improves the fault tolerance of systolic arrays (applicable to scenarios with a higher number of faulty PEs) but also reduces circuit areas. Therefore, the proposed approach proves effective in practical applications.

Spectral Characteristics Analysis of Images Matrix Masking Results

The article describes the results of a computational experiment to assess the capabilities of extracting useful information if an image masked by quasi-orthogonal matrices sent over an open channel became available to a third party. Hadamard and Mersenne matrices of symmetric and cyclic structure are considered. The results confirm the data that images masked by small-sized matrix leaves edges of the original image on the masked image. However, with an increase in the size of the masking matrix, all considered in the article matrices reliably hides the original image during visual analysis. Masking by symmetric Mersenne-Walsh matrices and cyclic Mersenne matrices based on modified M-sequences provides better spectral secrecy of masked images in comparison with Hadamard matrices. Mersenne matrices of cyclic structure, with equal sizes of the image and the masking matrix, bring the phase spectrum of the masked image to a form close in spectrum to uniform noise, which makes their use more preferable based on the considerations that the human visual system is extremely sensitive to phase-frequency distortions of the visual information.

Two-pronged feature reduction in spectral clustering with optimized landmark selection

Spectral clustering is widely employed for clustering data points, particularly for non-linear and non-convex structures in high-dimensional spaces. However, it faces challenges due to the high computational cost of eigen decomposition operations and the performance limitations with high-dimensional data. In this paper, we introduce BVA_LSC, a novel spectral clustering algorithm designed to address these challenges. Firstly, we incorporate an advanced feature reduction stage utilizing Barnes-Hut t-SNE and a deep Variational Autoencoder (VAE) to efficiently reduce the dimensionality of the data, thereby accelerating eigen decomposition. Secondly, we propose an adaptive landmark selection strategy that combines the Grey Wolf Optimizer (GWO) with a novel objective function and K-harmonic means clustering. This strategy dynamically determines an optimal number of landmarks, enhancing the representativeness of the data and reducing the size of the similarity matrix. We assess the performance of our algorithm on various standard datasets, demonstrating its superiority over state-of-the-art methods in terms of accuracy and efficiency.

Adaptive Pixel-Based Technique for Grayscale Image Compression

Grayscale images are extensively used due to their simplicity and cheapness in storage and transmission compared to color one of RGB base. It can also be considered a solution for color-blind people to ensure a better view of things and reading. However, unfortunately, it is still quite overburdened with redundancy(s) in which the data compression exploits them efficiently depending on the type and way of redundancy removal. This work introduces a hybrid compression system to compress grayscale images using the adaptive pixel-based technique (PBT) of optimized modeling base, with incorporated Minimize Matrix Size Algorithm (MMSA) of three digits values (C321) to encode the residual compactly along the need to overhead information (index, mean). Adapting traditional PBT led to overcoming the problems in the conventional PBT system in terms of large size. It achieved an acceptable reduction in bytes for the deterministic part (M, Indx) of over 400 bytes and the deterministic part (Res), where the size was reduced to more than 5000 bytes on average. The size has been reduced by nearly 50% compared to traditional PBT. The tested results indicate higher quality compared to the standard JPEG and traditional PBT in terms of performance. This includes a Compression Ratio (CR) of 13 and a PSNR of 48 dB.