Digital Signal Processing

Scientific & Technical

“Digital Signal Processing” No. 4-2021

Digital image processing
In the issue:

- Radar imaging
- hyperspectral images analysis
- noisy radar images classification
- object image contours rediscretization
- corresponding objects search algorithm
- accuracy estimation of images stitching
- organization of remote sensing imaging systems calibration
- neural network polyp detector on video images
- design quantized pulse-shaping FIR filters
- analysis of the codes soft decoding method

Design quantized pulse-shaping FIR filters for digital communication systems
Mingazin A.T., e-mail:

RADIS Ltd, Russia, Moscow

Keywords: quantized pulse-shaping linear-phase FIR filters, square-root raised cosine filters, weighted Chebyshev approximation, inter-symbol interference, variation of initial parameters.

Three significantly different design methods of matched quantized pulse-shaping linear-phase FIR filters of direct structure for digital communication systems are considered. The first is based on obtaining a frequency characteristic of the square-root raised cosine form, and the second and third are based on a weighted Chebyshev approximation of a magnitude response. The third method corresponds to a two-step approximation for a half-band filter and an amplitude corrector, the cascade connection of which forms a pulse-shaping filter. The design by each method is aimed at achieving the required values of stopband attenuation of magnitude response for the pulse-shaping filter and the ISI level at the output of the cascade connection of a pair of such filters at minimum values of the order and coefficient wordlength. The problem of coefficient quantization in each of the methods is solved by using the technique of variation of initial parameters, which is illustrated graphically. Results of the filter design for two values of roll-off factor 0.35 and 0.05 at the oversampling factor equal to 2 are presented.

All the results obtained by the three methods satisfy the specified requirements for attenuation in the stopband (≥50 dB) and ISI (≤-25 dB) at close values of the coefficient wordlength differing by no more than 1 bit for each of the two values of the roll-off factor. The second and third methods in comparison with the first result in a significantly smaller number of multipliers and adders in the filter structures. The second - allows you to obtain smaller orders of filters and, therefore, the smallest group delay values. According to the level of peak-to-average power ratio of the modulated signal, the results have a spread of 4.2-5.5 dB and 7.8-9.9 dB, respectively, for roll-off factors 0.35 and 0.05. The lower limits of this parameter are achieved by the second method.

How good are the obtained quantized pulse-shaping FIR filters in combination with possible additional interpolation/decimation steps in specific digital communication systems in the presence of timing jitter, noise, interference and non-linear distortions can be ascertained by mathematical and/or physical modeling.


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Increasing the efficiency of the signals processing in case of continuous wave interference by choosing the function of the preliminary weighting for frequency notch
E.V. Kuzmin, e-mail:

Siberian Federal University (SibFU), Russia, Krasnoyarsk

Keywords: signals searching, continuous wave interference, frequency notch, weight function, discrete Fourier transform.


The efficiency of the spread spectrum signal delay searching is investigated for the suppres-sion of an intense additive continuous wave interference due to frequency rejection based on the discrete Fourier transform. To reduce the influence of the "pedestal effect" on the quality of processing, the weight (window) functions of Hann, Blackman, Parzen (de la Valle-Poussin), Henning and some others are considered. Statistical experiments have established and demonstrated an in-crease in the efficiency of spread spectrum signal searching under these conditions when using power-law variations of the Henning window (in comparison with others considered). The article presents curves of dependences of the probability of correct signal searching for various reception conditions and typical variants of the produced coherent accumulations.

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Analysis of the method of soft decoding of error-correcting codes
M.A. Bykhovskiy, e-mail:

Moscow Technical University of Communications and Informatics, Russia, Moscow

Keywords: Noise-immune codes, hard decoding, soft decoding, Shannon's threshold, energy efficiency of communication systems, two-dimensional and multi-dimensional signal ensembles.

The paper proposes a new method of soft decoding of a code combination of an error-correcting code and a method for determining the reliability of communication with a hard (HDD) and soft (SDD) method for decoding an error-correcting code (PC), which depends on the marginal speed of signal transmission (Rf) belonging to AS with QAM, and the code speed (Rc) of the PC. It is demonstrated that for small values of (Rc) application of the SDD method provides energy gain equal to 2 dB as compared to the HDD method. This gain diminishes to 1 dB at high (Rc) values. The author provides recommendations on how to choose energy parameters of the communication system that would allow to reduce the length of the code for a given reliability of message reception, essentially without increasing the energy power of the communication line.

Possible energy losses of communication systems with a PC as compared to the Shannon limit are introduced. It is demonstrated that these losses can be insignificant only for low-speed communication systems. For high-speed communication systems, they turn out to be rather material, especially when using a PC with a low code speed. It is noted that in promising communication systems intended for the transmission of messages with high speed and high energy efficiency, it is advisable to use multidimensional AS that are optimal according to Shannon, which make it possible to ensure high reliability of message reception without the application of error-correcting codes.

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Algorithm for generating detailed radar images with compensation of flight's trajectory instabilities of the SAR's carrier by the leeway
N.P. Muraviev, e-mail:
L.B. Ryazantsev,

MESC «Zhukovsky–Gagarin Air Force Academy», Russia, Voronezh

Keywords: synthetic aperture radar, trajectory instability, leeway, radar images.

Recently, there has been an active use of radar equipment on small-sized unmanned aerial vehicles (UAVs) to solve problems of aerial monitoring, mapping, communications control and other tasks in the military and civil sphere. Existing technologies of digital signal processing through the use of methods of synthesizing the antenna aperture make it possible to realize the formation of ra-dar images with high spatial resolution in units of decimeters and in close to real time, and miniatur-ization technologies make it possible to reduce the weight and size characteristics of the equipment to several kilograms, which allows them to be installed on small-sized UAVs, including multicop-ters. Despite the high potential capabilities of such radars, obtaining detailed radar images is associ-ated with significant computational costs, which significantly increase in the presence of trajectory instability of the radar carrier flight. So, with a rigidly fixed antenna and the lack of control over the position of the beam of the directional pattern in the azimuthal plane, which is typical when in-stalling radar on small-sized UAVs, the presence of a crosswind leads to a change in the angle of drift and deviation of the beam of the antenna pattern from the direction perpendicular to the carrier velocity vector. This leads to the fact that when implementing algorithms for the formation of radar images, which are very demanding on the performance of on-board computers, it is necessary to significantly increase the size of the image frame along the travel distance. Since the brightness of the radar images resolution elements is calculated within the entire frame, including those that do not fall into the beam of the radar radiation pattern, this leads to a proportional increase in computa-tional costs and time for the formation of the radar image frame. In addition, the constant change in the position of the beam of the directional pattern during the flight of the carrier significantly com-plicates the implementation of the strip mode of shooting, and non-zero brightness values of resolu-tion elements due to side lobes and ambiguity zones located outside the main beam of the radar di-rectional pattern have a negative impact on the quality of the automatic focusing algorithms of the radar images.

Thus, the article is devoted to the development of an algorithm that provides up to two... three times declined the computational costs of the on-board computer when generating radar imag-es by excluding image elements from the calculation that are not included in the main beam of the antenna pattern. The calculation of the elements is carried out taking into account the presence of trajectory instabilities in the angle of demolition caused by a crosswind during the flight of a small-sized unmanned aerial vehicle. The leeway is determined based on an estimate of the average Dop-pler frequency in the signal at the output of the radar receiver.

The results of the algorithm study showed that the proposed algorithm provides a two- to three-fold reduction in the time spent on the formation of a radar image in the presence of trajectory flight instability along the drift angle. Moreover, the greater the value of the drift angle– the greater the gain in the time of formation of the radar image is observed. This is due to an increase in the size of the frame at large values of the drift angle. Along with reducing the time of radar image for-mation, the use of geometric correction procedures makes it possible to improve the quality of au-tomatic focusing algorithms, simplify the procedure for further georeferencing images to digital ter-rain maps, and also improve the perception of images by the decoder operator.

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8. Kolchinskij V.E., Mandurovskij I.A., Konstantinovskij M.I. Avtonomnye doplerovskie ustrojstva i sistemy navigacii letatel'nyh apparatov (Autonomous Doppler devices and aircraft navi-gation systems) / Pod red. V.E. Kolchinskogo. M.: Sov. radio, 1975. 432 s.

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Correlation and structural analysis of the gradient spectrum of hyperspectral images in the problem of spectral selection of contours of given objects

V.V. Shipko, e-mail:
MESC AF «N.E. Zhukovsky and Y.A. Gagarin Air Force Academy», Russia, Voronezh

Keywords: hyperspectral images, gradient, correlation function, structural function, random functions with stationary increments

As it is known, an important intermediate stage of the set of final tasks of digital image pro-cessing is the selection of the contours of objects. The use of contour images can significantly re-duce the computational costs of various algorithms for subsequent analysis and recognition, which is especially important for processing multicomponent hyperspectral images. There are many methods and algorithms for contour selection on single-component images, however, the classical approach of contour selection in each spectral component and their component analysis are ineffective for multicomponent hyperspectral images. This is mainly due to the lack of the possibility of taking into account the relationship between spectral components. Analyzing sequentially the contours of each spectral channel is a laborious and inefficient task, and averaging the results obtained leads to the loss of valuable information about the spectral relationship.

Therefore, it is of interest to obtain an extended (functional) relationship of each component of the gradients with respect to all other components for the possibility of more flexible contour se-lection. Taking into account the presence of gradients of each spectral component of the GSI, which in themselves are a spatial characteristic of brightness differences, we will consider the correlation and structural functions as their functional relationship.

The efficiency of correlation and structural functions in the task of selecting the contours of spectral-selective objects on hyperspectral images has been studied. The results obtained indicate a higher noise immunity and informativeness of the structural function compared to the correlation function. An approach to the synthesis of an optimal algorithm for the selection of contours of spec-tral-selective objects based on the distribution densities of the values of the structural function of spectral gradient images is proposed.

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Visualization of convolutional neural network patterns in the noisy radar images classification problem
Kupryashkin I.F., e-mail:
Mazin A.S., e-mail:
Military Educational and Scientific Center of the Air Force “N.E.Zhukovsky and Y.A.Gagarin Air Force Academy”, Russia, Voronezh

synthetic aperture radar, deep convolutional neural network, object classification.

It is known that deep convolutional neural networks (DCNN) are successfully used for object recognition on radar images. However, to date, insufficient attention is paid to the study of the accuracy of object marks classification under the radar interference influence.

The article describes the results of a study on the efficiency of object marks classification by a deep convolutional neural network under the intentional radar interference influence.

The article deals with an algorithm of training data preparation procedure, a description of input images (pattern), providing maximum activation of convolution layer filters at different interference (noise) intensities, as well as evaluation of classification accuracy of ground object marks on radar images at different interference/signal ratios on training and test sets

The procedure of training data preparation includes elimination of surface marks (terrain back-ground) on the MSTAR radar images set, decreasing the size of images to the objects size and addition of image noise.

From comparison of the received input images (patterns), providing maximum activation of the convolutional network filters, trained on a set of images without interference and on a set with interference/signal ratio q=0 dB, it is clear that under the interference influence the texture diversity of the features in higher layers became much smaller, and the patterns themselves - more homogeneous. This fact proves the decrease of the network sensitivity to the classification features of a particular set of images under the influence of interference.

The influence of interference is quite expectedly manifested in a decrease in the accuracy of classification of object marks on the radar images. The maximum accuracy value in an interference-free condition is 97.91%, at an interference level comparable to the average level of object marks (q = 0 dB) it remains quite high - 86.13%, but with a further increase in the signal-to-noise ratio it decreases rapidly. For example, if the q = 5 dB a correct network operation is seen in about a half of cases (55,01 %), and if the q = 15 dB and more - 13,18 %, that practically comes down to a simple guess (for the ten-alternative classification the accuracy is about 10 %).

1. Zhu X., Montazeri S., Ali M., Hua Yu., Wang Yu., Mou L., Shi Yi., Xu F., Bamler R. Deep Learn-ing Meets SAR. arXiv:2006.10027v2 [eess.IV] 5 Jan 2021.

2. Wang H., Chen S., Xu F., Jin Y.-Q. Application of Deep-Learning Algorithms to MSTAR Data. 2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 2015, pp. 3743-3745. DOI: 10.1109/IGARSS. 2015.7326637.

3. Chen S., Wang H., Xu F., Jin Y.-Q. Target Classification Using the Deep Convolutional Networks for SAR Images. IEEE Transaction Geoscience and Remote Sensing, 2016, vol. 54, no. 8, pp. 4806-4817. DOI: 10.1109/TGRS. 2016.2551720.

4. Anas H., Majdoulayne H., Chaimae A., Nabil S.M. Deep Learning for SAR Image Classification. 2020. DOI: 10.1007/978-3-030-29516-5_67.

5. Chen S., Wang H. SAR Target Recognition Based on Deep Learning. 2014 International Conference on Data Science and Advanced Analytics (DSAA), 2014, pp. 541-547. DOI: 10.1109/DSAA.2014.7058124.

6. Coman C., Thaens R. A Deep Learning SAR Target Classification Experiment on MSTAR Dataset. 2018 19th International Radar Symposium (IRS), 2018, pp. 1-6. DOI: 10.23919/IRS.2018.8448048.

7. Furukawa H. Deep Learning for End-to-End Automatic Target Recognition from Syn-thetic Aperture Radar Imagery. arXiv:1801.08558v1 [cs.CV] 25 Jan 2018.

8. Profeta A., Rodriguez A., Clouse H.S. Convolutional Neural Networks for Synthetic Ap-erture Radar Classification. Proc. SPIE 9843, Algorithms for Synthetic Aperture Radar Imagery XXIII, 98430M (14 May 2016).

9. Borodinov A.A., Myasnikov V.V. Comparison of radar image classification algorithms for various preprocessing methods based on MSTAR data. IV International Conference and Youth School "Information Technologies and Nanotechnologies" (ITNT-2018).

10. Zhang C., Li P., Sun G., Guan Y., Xiao B., Cong J. Optimizing FPGA-based accelerator design for deep convolutional neural networks. Proceedings of the 2015 ACM/SIGDA Internation-al Symposium on Field Programmable Gate Arrays, 2015.pp. 161-170. DOI: 10.1145/2684746.2689060.

11. I.V. Zoev, N.G. Markov, A.P. Beresnev, T.A. Yagunov. FPGA-based hardware imple-mentation of convolution neural networks for images recognition. GraphiCon, 2018. pp. 200-203.

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Rediscretization the contours of digital images of objects

Okhotnikov S.A., e-mail:
Khafizov D.G., e-mail:
Egoshina I.L., e-mail:
Khafizov R.G.,, e-mail:
The Volga State Technological University (VSUT, Volgatech), Russia, Yoshkar-Ola

Keywords: rediscretization, equalization, spectrum shape consistency, alignment of the contour dimensions.

The article deals with the issues of changing the dimensionality of the contours of digital images of objects. Contour image analysis is one of the effective methods of image processing which has a number of advantages over stream processing, including the ability to switch from two-dimensional to one-dimensional processing. The use of the normalized scalar product of image contours as a measure of similarity makes it possible to construct processing algorithms invariant to linear transformations of images. However, the calculation of the normalized scalar product requires the alignment of the dimensions of the analyzed contours.

When evaluating resampling methods, continuous complex-valued contours on the complex plane were specified as reference images, followed by their discretization. In the next step the dimension alignment procedure was performed. The normalized scalar product of the contours was used to determine the similarity measure.

Simulation results show that the method of maximum preservation of the contour spectrum realized by the scheme "interpolation - filtering - thinning" provides the value of the normalized scalar product of the contours close to the value of the normalized scalar product of the original continuous contours. In addition, the value of the normalized scalar product of contours at decreasing the dimensionality is higher than at oversampling with increasing the dimensionality.

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Corresponding objects search algorithm in Earth remote sensing images aware of low-informative areas
A.E. Kuznetsov, e-mail:
A.S. Ryzhikov
, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: corresponding objects, Earth remote sensing images, low-informative areas, GPU, CPU.

Increasing performance of the algorithm for corresponding objects search on analyzed and reference images by preliminary rejection of low-informative areas is investigated. Computationally simple methods for revealing textured homogeneous fragments on image are considered. The results of the experimental use of the modified search algorithm for corresponding objects are presented. Detection of low-informative areas is carried out at the preliminary stage of the algorithm. Further, the search for objects with the same name was carried out only in informative areas.

In terms of the ratio calculation speed / proportion of excessively rejected the same name objects, the algorithm for constructing a mask of low-informative areas based on difference of Gaussians has proven to be optimal. The sample size of successfully identified the same name objects in most cases is sufficient to solve the problem. Also, it is comparable with the standard algorithm but provides significantly better performance.

Unfortunately, all the considered algorithms for determining low-informative areas showed unsatisfactory results in the problem of detecting cloud objects. In this regard, it is recommended to use specialized solutions for detecting cloud objects. The issue of fast rejection of cloud objects is planned to be considered in the next work.

1. Kuznetsov A.E., Poshehonov V.I., Ryzhikov A.S. Tehnologija avtomaticheskogo kontrolja tochnosti geoprivjazki sputnikovyh izobrazhenij po opornym snimkam ot KA «Landsat-8» // Öèô-ðîâàÿ îáðàáîòêà ñèãíàëîâ, 2015, no. 3, pp. 37-42.

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A priori estimation of accuracy of TDI CCD images stitching based on spacecraft measurement equipment data
O.A. Presnyakov, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: remote sensing, stitching accuracy, staggered TDI CCD.

This article presents the method for geometric accuracy apriori estimation in the task of stitching of satellite images obtained by staggered TDI CCD. The method can be applied in design of spacecraft cameras to check the ability of automatic images stitching based on spacecraft measurement equipment data.

The method uses the following parameters: Earth parameters, apogee and perigee of the satellite orbit, look angle, spacecraft measurement equipment accuracy (the number, precision and placement of star trackers, precision of angular velocity sensors), interior orientation parameters (focus, pixel size, distance between rows of even and odd CCDs, photozone width, CCD position estimation accuracy), accuracy of DEM, satellite vibration amplitude, geometric processing accuracy. The error of the satellite spatial position determining is assumed to be negligible to affect the stitching.

The displacement of images from neighboring CCDs (scans) have a complex form. It is caused by the fact that one ground point is shot by neighboring matrices with a certain time interval. During this time, the orientation of the spacecraft changes, the Earth rotates, and the spacecraft moves in orbit. Due to movement along the orbit, among other things, parallactic distortions between scans appears.

To estimate the total stitching error, the orbital velocity of the satellite and the interval between shooting one point by neighboring CCDs are first calculated. Using this interval, the influence of the angular velocity measurement random error on the stitching is determined. Then, the total accuracy of the spacecraft orientation angles measuring using star trackers is found, taking into account star trackers relative position. Using the orientation measurement error, the error of the angular velocity sensors “drift” and the stitching error caused by it are found. Next, the stitching errors due to DEM error, CCD placement error and geometric processing error are calculated. Stitching error due to vibrations is then evaluated. Stitching error due to vibrations of a known frequency and amplitude, which may not be foreseen in advance, is considered separately; such distortions was detected in the “Aist-2D” small spacecraft images using spectral analysis. Finally, the errors from all considered factors are summarized.

The method has been tested on real images from “Aist-2D” small spacecraft. The test results confirmed the adequacy of the proposed model.

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Organization of remote sensing imaging systems geometric calibration
A.E. Kuznetsov, e-mail:
V.I. Poshekhonov, e-mail:

The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: remote sensing camera, star tracker, ground control points, exterior and interior orientation parameters.

The technological scheme of the in-flight geometric calibration of Earth remote sensing systems is considered. The technology includes two stages of calibration activities. The first stage is performed during the satellite flight tests and is associated with the refinement of the interior orientation parameters and the mounting angles of the camera. Formulas are given to refine the relative orientation of star trackers based on a set of their measurements. The task of the second stage is to monitor the mounting angles of the camera. It is shown that the recalibration process should be performed in case of exceeding the permissible misalignment of measurements by star trackers of the camera orientation roll, pitch and yaw angles. A model justifying the number of calibration routes that are necessary during calibration process is given. A conclusion is given on the practical use of the considered technological process and the ways of its improvement.

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