Recovery Error Research Articles

CHAOTIC COMPRESSIVE SENSING OF TV –UHF BAND IN IRAQ USING CHEBYSHEV GRAM SCHMIDT SENSING MATRIX

Cognitive radio (CR) is a promising technology for solving spectrum sacristy problem. Spectrum sensing is the main step of CR. Sensing the wideband spectrum produces more challenges. Compressive sensing (CS) is a technology used as spectrum sening in CR to solve these challenges. CS consists of three stages: sparse representation, encoding and decoding. In encoding stage sensing matrix are required, and it plays an important role for performance of CS. The design of efficient sensing matrix requires achieving low mutual coherence . In decoding stage the recovery algorithm is applied to reconstruct a sparse signal. İn this paper a new chaotic matrix is proposed based on Chebyshev map and modified gram Schmidt (MGS). The CS based proposed matrix is applied for sensing real TV signal as a PU. The proposed system is tested under two types of recovery algorithms. The performance of CS based proposed matrix is measured using recovery error (Re), mean square error (MSE), and probability of detection (Pd) and evaluated by comparing it with Gaussian, Bernoulli and chaotic matrix in the literature. The simulation results show that the proposed system has low Re and high Pd under low SNR values and has low MSE with high compression.

Recovery of continuous functions of two variables from their Fourier coefficients known with error

In this paper, we continue to study the classical problem of optimal recovery for the classes of continuous functions. The investigated classes $W^{\psi}_{2,p}$, $1 \leq p < \infty$, consist of functions that are given in terms of generalized smoothness $\psi$. Namely, we consider the two-dimensional case which complements the recent results from [Res. Math. 2020, 28 (2), 24-34] for the classes $W^{\psi}_p$ of univariate functions.
 As to available information, we are given the noisy Fourier coefficients $y^{\delta}_{i,j} = y_{i,j} + \delta \xi_{i,j}$, $\delta \in (0,1)$, $i,j = 1,2, \dots$, of functions with respect to certain orthonormal system $\{ \varphi_{i,j} \}_{i,j=1}^{\infty}$, where the noise level is small in the sense of the norm of the space $l_p$, $1 \leq p < \infty$, of double sequences $\xi=( \xi_{i,j} )_{i,j=1}^{\infty}$ of real numbers. As a recovery method, we use the so-called $\Lambda$-method of summation given by certain two-dimensional triangular numerical matrix $\Lambda = \{ \lambda_{i,j}^n \}_{i,j=1}^n$, where $n$ is a natural number associated with the sequence $\psi$ that define smoothness of the investigated functions. The recovery error is estimated in the norm of the space $C ([0,1]^2)$ of continuous on $[0,1]^2$ functions.
 We showed, that for $1\leq p < \infty$, under the respective assumptions on the smoothness parameter $\psi$ and the elements of the matrix $\Lambda$, it holds \[ \Delta( W^{\psi}_{2,p}, \Lambda, l_p)= \sup\limits_{ y \in W^{\psi}_{2,p} } \sup\limits_{\| \xi \|_{l_p} \leq 1} \Big\| y - \sum\limits_{i=1}^{n} \sum\limits_{j=1}^{n} \lambda_{i,j}^n ( y_{i,j} + \delta \xi_{i,j}) \varphi_{i,j} \Big\|_{C ([0,1]^2)} \ll \frac{ n^{\beta + 1 - 1/{p}}}{\psi(n)}.\]

Recovery analysis for ℓ2/ℓ1−2 minimization via prior support information

This paper discusses the block sparse signal recovery when the partial prior support information is available. A high order block RIP condition for our proposed weighted ℓ2/ℓ1−2 minimization is established, which in absence of support information is proved to improve the previous one. We demonstrate that the obtained recovery condition is weaker than the analogous one for ℓ2/ℓ1−2 minimization if at least 50% of the estimated block support information is accurate, and the corresponding recovery error estimate is also better. In addition, a series of numerical experiments are carried out to show the excellent recovery performance of the weighted ℓ2/ℓ1−2 minimization.

Machine-learning nonconservative dynamics for new-physics detection.

Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our neural new-physics detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and nonconservative components, which are represented by a Lagrangian neural network (LNN) and an unconstrained neural network, respectively, trained to minimize the force recovery error plus a constant λ times the magnitude of the predicted nonconservative force. We show that a phase transition occurs at λ=1, universally for arbitrary forces. We demonstrate that NNPhD successfully discovers new physics in toy numerical experiments, rediscovering friction (1493) from a damped double pendulum, Neptune from Uranus' orbit (1846), and gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD coupled with an integrator outperforms both an LNN and an unconstrained neural network for predicting the future of a damped double pendulum.

On Recovery of Sparse Signals With Prior Support Information via Weighted ℓₚ-Minimization

A complete characterization for the restricted isometry constant (RIC) bounds on $\delta _{{{ tk}}}$ for all $ {t}>0$ is an important problem on recovery of sparse signals with prior support information via weighted $\ell _{{p}}$ -minimization ( $0 ). In this paper, new bounds on the restricted isometry constants $\delta _{{{ tk}}}$ ( $0 ), where $d$ is a key constant determined by prior support information, are established to guarantee the sparse signal recovery via the weighted $\ell _{{p}}$ minimization in both noiseless and noisy settings. This result fills a vacancy on $\delta _{{{ tk}}}$ with $0 , compared with previous works on $\delta _{{{ tk}}}$ ( ${t} \geqslant \frac {4}3{d}$ ). We show that, when the accuracy of prior support estimate is at least 50%, the new recovery condition in terms of $\delta _{{{ tk}}}$ ( $0 ) via weighted $\ell _{1}$ minimization is weaker than the condition required by classical $\ell _{1}$ minimization without weighting. Our weighted $\ell _{1}$ minimization gives better recovery error bounds in noisy setting. Similarly, the new recovery condition in terms of $\delta _{{{ tk}}}$ ( $0 ) is extended to weighted $\ell _{{p}}$ ( $0 ) minimization, and it is also weaker than the condition obtained by standard non-convex $\ell _{{p}}$ ( $0 ) minimization without weighting. Numerical illustrations are provided to demonstrate our new theoretical results.

Nearly optimal number of iterations for sparse signal recovery with orthogonal multi-matching pursuit * *This work was partially supported by the National Natural Science Foundation of China (Grant nos. 61907014, 11871248, 11701410, 61901160), the Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2019), Guangdong Major Project of Basic and Applied Basic Research (2019B030302008), the Natural Science Foundation of

A signal x is called K-sparse if it has at most K nonzero entries. Recovering a K-sparse signal x from linear measurements y = Ax + w, where A is a sensing matrix and w is a noise vector, arises from numerous applications. Orthogonal multi-matching pursuit (OMMP), which is an extension of the orthogonal matching pursuit (OMP) algorithm and has better recovery performance than OMP, is a popular sparse recovery algorithm. One of the main challenges to study the recovery performance of OMMP is to investigate the optimal required number of iterations for ensuring stable reconstruction of x. This paper provides a nearly optimal number of iterations. Specifically, based on the restricted isometry property of the sensing matrix, we present a sufficient condition that can guarantee stable reconstruction of x in nearly optimal number of iterations by OMMP. Furthermore, we build an upper bound on the recovery error with fewer required iterations than existing results. Our results show that the required number of iterations to ensure stable recovery of any K-sparse signals is fewer than those required by the state-of-the-art results.

Highly Efficient Spatial-Temporal Correlation Basis for 5G IoT Networks.

One of the major concerns in 5G IoT networks is that most of the sensor nodes are powered through limited lifetime, which seriously affects the performance of the networks. In this article, Compressive sensing (CS) technique is used to decrease transmission cost in 5G IoT networks. Sparse basis is one of the important steps in the CS. However, most of the existing sparse basis-based method such as DCT (Discrete cosine transform) and DFT (Discrete Fourier Transform) basis do not capture data structure characteristics in the networks. They also do not take into consideration multi-resolution representations. In addition, some of sparse basis-driven methods exploit either spatial or temporal features, resulting in performance degradation of CS-based strategies. To address these challenging problems, we propose a novel spatial–temporal correlation basis algorithm (SCBA). Subsequently, an optimal basis algorithm (OBA) is provided considering greedy scoring criteria. To evaluate the efficiency of OBA, orthogonal wavelet basis algorithm (OWBA) by employing NS (Numerical Sparsity) and GI (Gini Index) sparse metrics is also presented. In addition, we discuss the complexity of the above three algorithms, and prove that OBA has low numerical rank. After experimental evaluation, we found that OBA is capable of the sparsest representing original signal compared to spatial, DCT, haar-1, haar-2, and rbio5.5. Furthermore, OBA has the low recovery error and the highest efficiency.

Non-Markovian memory strength bounds quantum process recoverability

Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovian phenomena, enabling compression and recovery techniques pivotal to near-term technologies. We highlight the implications of our results by analyzing an exactly solvable model to show that memory truncation is possible even in a highly non-Markovian regime.

A chirplet transform-based mode retrieval method for multicomponent signals with crossover instantaneous frequencies

In nature and engineering world, the acquired signals are usually affected by multiple complicated factors and appear as multicomponent nonstationary modes. In such and many other situations, it is necessary to separate these signals into a finite number of monocomponents to represent the intrinsic modes and underlying dynamics implicated in the source signals. In this paper, we consider the mode retrieval of a multicomponent signal which has crossing instantaneous frequencies (IFs), meaning that some of the components of the signal overlap in the time-frequency domain. We use the chirplet transform (CT) to represent a multicomponent signal in the three-dimensional space of time, frequency and chirp rate and introduce a CT-based signal separation scheme (CT3S) to retrieve modes. In addition, we analyze the error bounds for IF estimation and component recovery with this scheme. We also propose a matched-filter along certain specific time-frequency lines with respect to the chirp rate to make nonstationary signals be further separated and more concentrated in the three-dimensional space of CT. Furthermore, based on the approximation of source signals with linear chirps at any local time, we propose an innovative signal reconstruction algorithm, called the group filter-matched CT3S (GFCT3S), which also takes a group of components into consideration simultaneously. GFCT3S is suitable for signals with crossing IFs. It also decreases component recovery errors when the IFs curves of different components are not crossover, but fast-varying and close to each other. Numerical experiments on synthetic and real signals show our method is more accurate and consistent in signal separation than the empirical mode decomposition, synchrosqueezing transform, and other approaches.

Rapid simultaneous quantitative determination of linagliptin and empagliflozin as antidiabetic drugs using spectrophotometric method based on fuzzy systems and radial basis function neural network in tablet formulation and biological sample

In this study, spectrophotometry method was combined with artificial intelligence techniques for developing a simple, rapid, low-cost, and accurate approach for the simultaneous determination of Linagliptin (LIN) and Empagliflozin (EMPA) as antidiabetic drugs in mixtures and pharmaceutical formulation. Fuzzy inference system (FIS), adaptive Neuro-fuzzy inference system (ANFIS), and radial basis function neural network (RBF-NN) were proposed to predict the concentration of pharmaceutical components. The mean recovery and root mean square error (RMSE) of FIS were 98.44%, 103.50% and 0.0668, 0.1982 for LIN and EMPA, respectively. The mean recovery percentage of 100.07 and 99.83, as well as RMSE of 0.0033 and 0.0176 were obtained for LIN and EMPA, respectively. On the other hand, MSE related to the RBF-NN was found 1.46 × 10−26 and 1.72 × 10−25 for LIN and EMPA, respectively. Analysis of variance (ANOVA) test did not show a significant difference between high-performance liquid chromatography (HPLC) and proposed methods. The mean recovery (between 91.40% and 98.29%) and relative standard deviation (RSD) (lower than 0.5%) revealed that the suggested methods in a complex matrix such as urine had good predictive ability. Due to the obtained results, these methods can be used in quality control.

A method for optimal linear super-resolution image restoration

In this paper, we propose a super-resolution (pixel grid refinement) method for digital images. It is based on the linear filtering of a zero-padded discrete signal. We introduce a continuous-discrete observation model to create a reconstruction system. The proposed observation model is typical of real-world imaging systems - an initially continuous signal first undergoes linear (dynamic) distortions and then is subjected to sampling and the effect of additive noise. The proposed method is optimal in the sense of mean square recovery error minimization. In the theoretical part of the article, a general scheme of the linear super-resolution of the signal is presented and expressions for the impulse and frequency responses of the optimal reconstruction system are derived. An expression for the error of such restoration is also derived. For the sake of brevity, the entire description is presented for one-dimensional signals, but the obtained results can easily be generalized for the case of two-dimensional images. The experimental section of the paper is devoted to the analysis of the super-resolution reconstruction error depending on the parameters of the observation model. The significant superiority of the proposed method in terms of the reconstruction error is demonstrated in comparison with linear interpolation, which is usually used to refine the grid of image pixels.

NOISE IMMUNITY IN DATA COMPRESSION INFORMATION AND MEASUREMENT SYSTEMS

When processing huge data streams in information systems, individual measurements or whole groups of measurements can be distorted or lost due to various reasons. Recovery of compressed data during transmission on communication channels is accompanied by errors related to distortion of information and service parts of messages due to presence of interference in transmission channel. To these errors are added errors caused by quantization of the transmitted implementations by level and time sampling. Research on methods of increasing noise immunity both during transmission and during recovery of measured data is an urgent task in the design of information and measurement systems. The article considers non-parametric methods of estimating probabilistic characteristics of random processes. A distinctive feature of non-parametric methods is the ranking of data measured at the observation interval. It is shown that ranking of data on transmitting side of information-measuring system enables correction of errors and failures based on strict monotony of ranked number of codes. Also, the error of recovery of continuous implementations taking into account distortions of compressed data in the communication channel was investigated. The obtained results indicate that the use of complex compression algorithms is impractical, since the difference in the error in the restoration of non-stationary messages between the simplest algorithm and the rather difficult one becomes negligible. The article presents the results of estimating recovery errors for various data compression methods.

Estimating the lithospheric flexure of a plate with non-uniform flexural rigidity: a quantitative modelling approach

Lithospheric deformation is a fundamental process in plate tectonics. It is, therefore, critical to determine how the lithosphere responds to geological loads to better understand tectonic processes. The lithosphere can be modelled as the flexure of a thin, elastic plate over long-term (> 105 yr) geological timescales. The partial differential equation for the flexure of an orthotropic plate is used indirectly to calculate theoretical admittance and coherence, which are then compared against the observed admittance and coherence to invert for the non-uniform flexural rigidity (or effective elastic thickness, Te) of the plate. However, the process for accurately recovering variable lithospheric flexure remains unresolved, as the classical lithospheric model may overestimate the deflection of the plate. Here we adopt the classic lithospheric model with applied external and internal loads at the surface and Moho, respectively, and assume that the compensation material is denser than the mantle material beneath the Moho. The lithospheric flexure errors are derived mainly from the Te and Moho recovery errors in this lithospheric model. Synthetic modelling is then performed to analyse the influence of the Te and Moho errors. The analysis of synthetic modelling shows that: (1) the Te error-induced flexure errors exhibit a rippling pattern, and the rippling pattern is broader in high Te regions; (2) the Moho error-induced flexure errors mainly occur in the low Te regions, and applying Airy isostasy theory in low Te regions may still greatly overestimate the lithospheric deformation amplitude; and (3) the lithospheric flexure errors are dominated by the Te and Moho errors in the high and low Te regions, respectively.

Optimal selection of representative samples for efficient digital camera‐based spectra recovery

AbstractFor digital camera‐based spectra recovery, the spectral reflectance of the object being imaged always needs to be accurately recovered using training samples from available database. Considering the heavy workload when using all samples in database as training samples in practice, a new representative samples selection method is proposed for efficient digital camera‐based spectra recovery based on single RGB image. The representative simulation system is firstly constructed through correlation analysis of spectra recovery results of different systems, and based on the representative simulation system, a few number of representative samples are selected from the database based on minimum of the defined simulate spectra recovery error. The effectiveness of the proposed method is evaluated and compared with existing method. As the results show, the proposed method outperforms the existing methods, and the robustness of the selected representative samples is consistent with the database in practical applications.

A Pixel-Dependent Finite Element Model for Spatial Frequency Domain Imaging Using NIRFAST

Spatial frequency domain imaging (SFDI) utilizes the projection of spatially modulated light patterns upon biological tissues to obtain optical property maps for absorption and reduced scattering. Conventionally, both forward modeling and optical property recovery are performed using pixel-independent models, calculated via analytical solutions or Monte-Carlo-based look-up tables, both assuming a homogenous medium. The resulting recovered maps are limited for samples of high heterogeneity, where the homogenous assumption is not valid. NIRFAST, a FEM-based image modeling and reconstruction tool, simulates complex heterogeneous tissue optical interactions for single and multiwavelength systems. Based on the diffusion equation, NIRFAST has been adapted to perform pixel-dependent forward modeling for SFDI. Validation is performed within the spatially resolved domain, along with homogenous structured illumination simulations, with a recovery error of <2%. Heterogeneity is introduced through cylindrical anomalies, varying size, depth and optical property values, with recovery errors of <10%, as observed across a variety of simulations. This work demonstrates the importance of pixel-dependent light interaction modeling for SFDI and its role in quantitative accuracy. Here, a full raw image SFDI modeling tool is presented for heterogeneous samples, providing a mechanism towards a pixel-dependent SFDI image modeling and parameter recovery system.

Spectral sparse recovery form a single RGB image

An efficient procedure for spectral reflectance recovery using a new compressive sensing-based spectral sparse recovery method is proposed by using the optimized sparse basis functions to recover spectral reflectance from a single RGB image. Unlike the conventional spectral recovery methods, the sparse basis functions of the proposed method are an optimal solution for obtaining the information needed to consider the characteristics of the RGB response values. The novelty of the proposed method is to obtain the optimized sparse basis functions considering the influence of the spectral reflectance dataset and the sample’s colorimetric characteristic, which meets the minimum of the spectral recovery error. Spectral and colorimetric accuracy of the proposed method is studied to verify the effectiveness compared to existing methods. As the spectral recovery results show, the proposed method is extremely effective in recovering spectral reflectance.

Investigation of acquisition time for harmonization of image quality between PET/CT and PET/MRI systems: A phantom study

The positron emission tomography (PET) system has technological differences between PET/computed tomography (CT) and PET/magnetic resonance imaging (MRI). It is important to compare image quality on acquisition time for equal diagnostic performance. Therefore, the aim of study was to investigate acquisition time as a factor for harmonizing the image quality. NEMA image quality phantom experiments were performed using Siemens Biograph PET/CT and PET/MRI. The phantom was filled with 18F-solution at a 10:1 of sphere-to-background ratio and scanned in the list-mode. PET images were reconstructed with increasing time frames of 1 min. To compare image quality and measure difference, the contrast recovery (CR), background variability (BV), and measure root mean square error (RMSE) of BVs were used. PET/CT and PET/MRI showed similar CR for spheres regardless of acquisition time, whereas the BV was higher with PET/MRI than with PET/CT at the same acquisition time. The BV decreased with increasing acquisition time. The difference of BV by RMSE showed small values at an acquisition time delay of 2 min for PET/MRI. The PET images on visual analysis were also comparable at the lowest RMSE values. In conclusion, the image quality between PET/CT and PET/MRI was harmonized at a PET/MRI acquisition time of PET/CT acquisition time plus 2 min

Ultrasensitive determination of underivatized adamantane analogs in biological fluids by capillary electrophoresis with contactless conductivity detection

Separation techniques are promising for the detection of adamantane analogs with various functional groups. The derivatization of adamantane analogs with chromophores or fluorophores should be conducted using a separation technique combined with a common ultraviolet–visible or fluorescence detector. However, limited research has been conducted on underivatized adamantane analogs. Therefore, we present a highly rapid and sensitive method for detecting underivatized adamantane analogs by integrating ultrasound-assisted dispersive liquid–liquid microextraction (UADLLME), field-amplified sample stacking (FASS)-related capillary electrophoresis (CE), and capacitively coupled contactless conductivity detection (C4D). In the proposed system, UADLLME is used for sample clean up and analyte enrichment, whereas FASS-related CE provides on-line concentration of underivatized adamantane analogs during CE separation. A mixture of memantine (MT), amantadine (AT), and rimantadine (RT) was separated at baseline within 8 min through the application of optimized UADLLME (mixing extraction solvent, 50 μL of 1,1,2,2-tetrachloroethane (C2H2Cl4) and dispersive solvent, 200 μL of acetonitrile; mixing solution was injected into 1 mL of the sample solution at pH 12.5), FASS (buffer, 1.5 M acetic acid; additive, 0.05 mM β-cyclodextrin; pH 2.5), and C4D (amplitude, 2 Vpp; frequency, 500 kHz). The calibration curve exhibited acceptable linearity, with a coefficient of determination higher than 0.99. The limits of detection (signal-to-noise ratio of 3) were estimated to be 0.9, 1.0, and 1.2 nM for MT, AT, and RT, respectively. The relative standard deviations of peak areas varied from 8.9% to 9.3% (n = 5), whereas the sensitivity improvement of three underivatized adamantane analogs ranged from 1342 to 1766. The feasibility and accuracy of the present method for the determination of MT, AT, and RT in human serum and urine was satisfactorily confirmed by the excellent recovery and relative error. The proposed method exhibited high enrichment factors and offers excellent precision, high accuracy, and a short analysis time.

Development A Portable Solar Energy Measurement System

This project presents the design and development a portable measurement device for measure and monitor solar panel parameters by using Internet of Things (IoT) concept. Solar energy measurement plays a very important role in the measurement of parameter reading for the determination of output generated, but the challenge is only performed manually at the work site using a clamp meter or a multimeter. Furthermore, it was very difficult to get the value at that time, and the data recovery error occurred. There are three specific objectives have been used for the project. Firstly, the relevant circuits for this project are design and built the circuit by using software. The output of the measurement solar irradiance, ambient temperature, solar panel temperature, current and voltage value were displayed on LCD. Next, IoT concept is used for solar panel measurement and monitoring. The value of the measurement and monitoring is used ThingSpeak cloud and ThingView application on the smartphone. It can be collected the portable solar for the energy measurement system can monitor on site, anywhere and anytime using IoT platform.

АЛГОРИТМИЧЕСКО-ПРОГРАММНОЕ ОБЕСПЕЧЕНИЕ ДЛЯ ИСПОЛЬЗОВАНИЯ КУБИЧЕСКИХ СПЛАЙНОВ ПРИ ВОССТАНОВЛЕНИИ ФУНКЦИОНАЛЬНОЙ ЗАВИСИМОСТИ В СЛУЧАЕ ГРАНИЧНЫХ УСЛОВИЙ ДЛЯ ПЕРВЫХ ПРОИЗВОДНЫХ

The work is devoted to the creation of a cubic splineS (x), which ensures the restoration of the functional dependence Y(x) when specifying conditions for the first derivative of a function on the boundaries of its definition. It is assumed that the function Y(x) is continuous, has continuous first and second derivatives on the interval [a,b], and at the nodal points x0=a, x1, x2, ...,xn=b takes known values equal, respectively, y0, y1, y2,... yn, k=0, 1, 2,…, n. A spline is represented as n polynomials of order no higher than three. The problem is reduced to finding 4n unknown spline coefficients. To determine them, a system of 4n-2 equations was formed: 2n equations taking into account the values of the function at the nodal points, n-1 equations reflecting the continuity of the first derivative and n-1 equations reflecting the continuity of the second derivative at the boundaries of neighboring polynomials, as well as two conditions, related to the values of the first derivative at the boundaries of the function. Solving the problem by the sweep method allowed us to develop algorithmic software for constructing the corresponding cubic spline S(x) in the case of a continuous function Y(x) with continuous first and second derivatives on the segment [a,b] with given values of the first derivative on its boundaries. A scheme for implementing a solution in an algorithmic language is proposed. The Scype program was developed in the Microsoft Visual Studio shell using the C++ language. The magnitude of the function recovery error using the proposed scheme was studied using the example of the function Y(x)=sin (x). The test results showed that the relative accuracy of interpolation with the number of nodal points n=10 on the segment [0,π/2] averaged about 1.4 • 10-3. The maximum accuracy was found in the first interval: (0.4-0.9)10-3. The minimum accuracy is recorded at the beginning of the second and last tenth interval: (4-6)10-2. An increase in the number of nodes to 102, 103 and 104 led to an increase in the average relative accuracy to 1•10-5, 1•10-7 and 2• 10-9, respectively. The data obtained can be used to interpolate functions and process experimental data. Key words: function recovery algorithm, interpolation polynomial, interpolation, cubic spline.