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1

Image encryption algorithm based on rear-mounted phase mask and random decomposition

Yadav Shivani, Singh Hukum

Optica Applicata

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2022

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Vol. 52, nr 2

195--212

EN

To escalate the image encryption a new method has been devised which includes double random phase encoding (DRPE) using rear phase masking and random decomposition (RD) technique stranded on fractional Fourier transform. Here, asymmetric cryptographic system is developed in fractional Fourier transform (FrFT) mode using two random phase masks (RPM) and a rear mounted phase mask. In the projected scheme a colored image is decomposed into R, G and B channels. The amplitude of each channel is normalized, phase encoded and modulated using RPM. The modulated R, G and B channels of the colored image are individually transformed using FrFT to produce corresponding encrypted image. The proposed scheme is authorized on grayscale image also. The norm behind the development of the suggested scheme has been elaborated by carrying out cryptanalysis on system based on the RD. The method helps in escalations of the protection of double random phase encoding by cumulating the key length and the parameter amount, so that it vigorously can be used against various attacks. The forte of the suggested cryptographic system was verified using simulations with MATLAB 7.9.0 (R2008a). The efficiency of the suggested scheme includes the analysis using singular value decomposition (SVD), histogram and correlation coefficient.

2

Analysis of the possibility of using the singular value decomposition in image compression

Łukasik Edyta, Łabuć Emilia

Applied Computer Science

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2022

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Vol. 18, no. 4

53--67

EN

In today’s highly computerized world, data compression is a key issue to minimize the costs associated with data storage and transfer. In 2019, more than 70% of the data sent over the network were images. This paper analyses the feasibility of using the SVD algorithm in image compression and shows that it improves the efficiency of JPEG and JPEG2000 compression. Image matrices were decomposed using the SVD algorithm before compression. It has also been shown that as the image dimensions increase, the fraction of eigenvalues that must be used to reconstruct the image in good quality decreases. The study was carried out on a large and diverse set of images, more than 2500 images were examined. The results were analyzed based on criteria typical for the evaluation of numerical algorithms operating on matrices and image compression: compression ratio, size of compressed file, MSE, number of bad pixels, complexity, numerical stability, easiness of implementation.

3

Digital watermarking algorithm based on 4-level discrete wavelet transform and discrete fractional angular transform

Li Jing-You, Zhao Chun-Hui, Zhang Guang-Da

Optica Applicata

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2021

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Vol. 51, nr 4

605--619

EN

Nowadays, there are many watermarking algorithms based on wavelet transform. The simple one is to insert directly the watermark into the wavelet transform coefficients. However, most of the existing watermarking schemes can only resist traditional signal processing attacks, such as image compression, noise and filtering. When the watermarked image is subject to geometric transformations, especially rotation attack, it is hard to detect the watermark successfully. In this paper, a digital watermarking algorithm is proposed based on 4-level discrete wavelet transform and discrete fractional angular transform. To enhance the security of the algorithm, the watermark is scrambled with the simplicity of Arnold transform and chaos-based mix optical bistability model, since the chaos is pseudorandom and sensitive to the initial values. And the watermark is embedded into the medium frequency sub-band of the 1-level wavelet decomposition according to the Harris feature point detection. Simulation results show that the proposed digital watermarking algorithm by combining 4-level discrete wavelet transform with discrete fractional angular transform could resist rotation attack and other common attacks.

4

On the Singular Value Decomposition and Ranking Techniques

Zizler P., Thangarajah P., Sobhanzadeh M.

Computational Methods in Science and Technology

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2020

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Vol. 26, No. 1

15--20

EN

Let A be a positive non-singular n×n matrix. An approximation for a positive eigenvector for A∗A corresponding to the dominant singular value of A was suggested as the normalized version of a weighted sum of the rows of A with weights being the euclidean norms of the rows of A. In our paper we give a justification for this approach via the iteration of the power method and we show numerically that choosing the l1 norm yields better results. Applications of our results are given to ranking techniques.

5

Automated detection of Parkinson's disease using minimum average maximum tree and singular value decomposition method with vowels

Tuncer Turker, Dogan Sengul, Acharya Udyavara Rajendra

Biocybernetics and Biomedical Engineering

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2020

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Vol. 40, no. 1

211--220

EN

In this study, a novel method to automatically detect Parkinson's disease (PD) using vowels is proposed. A combination of minimum average maximum (MAMa) tree and singular value decomposition (SVD) are used to extract the salient features from the voice signals. A novel feature signal is constructed from 3 levels of MAMa tree in the preprocessing phase. The SVD operator is applied to the constructed signal for feature extraction. Then 50 most distinctive features are selected using relief feature selection technique. Finally, k nearest neighborhood (KNN) with 10-fold cross validation is used for the classification. We have achieved the highest classification accuracy rate of 92.46% using vowels with KNN classifier. The dataset used consists of 3 vowels for each person. To obtain individual results, post processing step is performed and best result of 96.83% is obtained with KNN classifier. The proposed method is ready to be tested with huge database and can aid the neurologists in the diagnosis of PD using vowels.

6

Effective algorithm for tomography imaging in threedimensional problems

Rymarczyk Tomasz, Sikora Jan, Adamkiewicz Przemysław

Przegląd Elektrotechniczny

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2019

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R. 95, nr 3

115--118

EN

This article presents a new effective imaging method that can be applied in ultrasonic and radio tomography. The proposed method by changing the shape of the voxels leads to a substantial simplification of the algorithm at the cost of small approximations of the voxels. As proved in the work, these approximations do not have a significant impact on the readability of the image which is several times faster.

PL

W pracy przedstawiono nową efektywną metodę obrazowania, która może mieć zastosowanie w transmisyjnej tomografii ultradźwiękowej lub radiowej. Proponowana metoda zmienia kształt voksela z sześciennego na kulisty dzięki czemu uzyskuje się znaczące uproszczenie algorytmu kosztem niewielkiej aproksymacji wokseli. Jak udowodniono w pracy, przyjęta aproksymacja nie ma znaczącego wpływu na wiarygodność obrazów, a jest kilkukrotnie bardziej efektywna.

7

Enhance the Capacity of MIMO Wireless Communication Channel using SVD and Optimal Power Allocation Algorithm

Kumar Neeraj, Kaur Dalveer

International Journal of Electronics and Telecommunications

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2019

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Vol. 65, No. 1

71--78

EN

Multiple input multiple output (MIMO) is a multiple antenna technology used extensively in wireless communication systems. With the ever increasing demand in high data rates, MIMO system is the necessity of wireless communication. In MIMO wireless communication system, where the multiple antennas are placed on base station and mobile station, the major problem is the constant power of base station, which has to be allocated to data streams optimally. This problem is referred as a power allocation problem. In this research, singular value decomposition (SVD) is used to decouple the MIMO system in the presence of channel state information (CSI) at the base station and forms parallel channels between base station and mobile station. This practice parallel channel ensures the simultaneous transmission of parallel data streams between base station and mobile station. Along with this, water filling algorithm is used in this research to allocate power to each data stream optimally. Further the relationship between the channel capacity of MIMO wireless system and the number of antennas at the base station and the mobile station is derived mathematically. The performance comparison of channel capacity for MIMO systems, both in the presence and absence of CSI is done. Finally, the effect of channel correlation because of antennas at the base stations and the mobile stations in the MIMO systems is also measured.

8

A fast neural network learning algorithm with approximate singular value decomposition

Jankowski Norbert, Linowiecki Rafał

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 3

581--594

EN

The learning of neural networks is becoming more and more important. Researchers have constructed dozens of learning algorithms, but it is still necessary to develop faster, more flexible, or more accurate learning algorithms. With fast learning we can examine more learning scenarios for a given problem, especially in the case of meta-learning. In this article we focus on the construction of a much faster learning algorithm and its modifications, especially for nonlinear versions of neural networks. The main idea of this algorithm lies in the usage of fast approximation of the Moore–Penrose pseudo-inverse matrix. The complexity of the original singular value decomposition algorithm is O(mn2). We consider algorithms with a complexity of O(mnl), where l < n and l is often significantly smaller than n. Such learning algorithms can be applied to the learning of radial basis function networks, extreme learning machines or deep ELMs, principal component analysis or even missing data imputation.

9

Efektywny algorytm obrazowania w tomografii ultradźwiękowej i radiowej dla zagadnień dwuwymiarowych

Rymarczyk T., Sikora J., Polakowski K., Adamkiewicz P.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 6

62--69

PL

W artykule przedstawiono nową efektywną metodę obrazowania, która może być zastosowana w tomografii ultradźwiękowej i radiowej. Proponowana metoda poprzez zmianę kształtu piksela prowadzi do znacznego uproszczenia algorytmu, kosztem niewielkich przybliżeń. Jak udowodniono w pracy, przybliżenia te nie mają istotnego znaczenia co do czytelności obrazu, kilkunastokrotnie przyspieszając jego uzyskanie.

XX

This article presents a new effective imaging method that can be applied in ultrasonic and radio tomography. The proposed method by changing the shape of the pixels leads to a substantial simplification of the algorithm at the cost of small approximations. As proved in the work, these approximations do not have a significant impact on the readability of the image which is several times faster.

10

Color image encryption using singular value decomposition in discrete cosine Stockwell transform domain

Vaish A., Kumar M.

Optica Applicata

|

2018

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Vol. 48, nr 1

25--38

EN

In this paper, an image encryption technique using singular value decomposition (SVD) and discrete cosine Stockwell transform (DCST) is proposed. The original source image is encrypted using bands of DCST along with the SVD decomposed images. The number of bands in DCST, parameters used to mask the singular values, the way of permutation used to shuffle the values of SVD transformed images and the way of arrangement of SVD matrices are used as encryption keys. It is necessary to have correct knowledge of all the keys along with their respective values, for correct decryption of encrypted images. The robustness and the quality measurement of proposed work are analyzed by comparing it with some existing works.

11

The chances of precision enhance for ultrasonic imaging

Rymarczyk T., Sikora J., Adamkiewicz P., Bożek P., Gołąbek M.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2018

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T. 8, nr 3

19--24

EN

The results of ultrasonic imaging with the aid of an algorithm with the virtual rays is presented in this paper. The signal associated with the virtual rays is calculated as an arithmetical mean value of the signals of the rays surrounding the virtual one. Developed algorithm was tested on synthetic free noise data then polluted synthetic data in order to move for the real measurements. Conclusions about the imaging with new algorithm are not obvious. In same cases the significant improvement was achieved but in some not.

PL

W pracy przedstawiono rezultaty działania algorytmu obrazowania ultradźwiękowego z dodatkowymi wirtualnymi promieniami. Sygnał odpowiadający wirtualnym promieniom jest wyliczany jako średnia arytmetyczna rzeczywistych sygnałów pomiarowych odpowiadających promieniom otaczającym dany promień wirtualny. Zaproponowany algorytm najpierw przetestowano na danych syntetycznych niezaszumionych, następnie na danych zaszumionych aby następnie przejść do danych pomiarowych. Wnioski na temat tego czy promienie wirtualne mają szanse podnieść jakość obrazowania nie są jednoznaczne. W niektórych przypadkach jakość jest znacznie lepsza a w innych nie.

12

Generalized Stockwell transform and SVD-based epileptic seizure detection in EEG using random forest

Zhang T., Chen W., Li M.

Biocybernetics and Biomedical Engineering

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2018

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Vol. 38, no. 3

519--534

EN

Purpose: Visual inspection of electroencephalogram (EEG) records by neurologist is the main diagnostic method of epilepsy but it is particularly time-consuming and expensive. Hence, it is of great significance to develop automatic seizure detection technique. Methods: In this work, a seizure detection approach, synthesizing generalized Stockwell transform (GST), singular value decomposition (SVD) and random forest, was proposed. Utilizing GST, the raw EEG was transformed into a time–frequency matrix, then the global and local singular values were extracted by SVD from the holistic and partitioned matrices of GST, respectively. Subsequently, four local parameters were calculated from each vector of local singular values. Finally, the global singular value vectors and local parameters were respectively fed into two random forest classifiers for classification, and the final category of a testing EEG was voted based on sub-labels obtained from the trained classifiers. Results: Four most common but challenging classification tasks of Bonn EEG database were investigated. The highest accuracies of 99.12%, 99.63%, 99.03% and 98.62% were achieved using our presented technique, respectively. Conclusions: Our proposed technique is comparable or superior to other up-to-date methods. The presented method is promising and able to handle with kinds of epileptic seizure detection tasks with satisfactory accuracy.

13

Hybrid Watermarking Algorithm using Finite Radon and Fractional Fourier Transform

Sharmaa J. B., Sharmaa K. K., Purohit S. D., Atangana A.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

523--543

EN

Watermarking is proposed as solution to authentication, copyright protection and security requirements of multimedia objects (speech, image and video). In this paper a watermarking scheme based on finite radon transform (FRAT), fractional Fourier Transform (FRFT) and singular value decomposition is proposed. In the proposed scheme, image to be watermarked is first transformed by finite radon transform, the radon transformed image is further transformed by FRFT, and singular values of FRFT transformed image are modified to embed the watermark. Inverse transformation is applied to obtain watermarked image. Simulations are performed under various test conditions with different FRFT transform angles for improved robustness and visual transparence of watermarked image. Results of the proposed scheme are better in comparison to the existing schemes for most of the attacks. Proposed scheme provide additional degree of freedom in security, robustness, payload capacity and visual transparence. Proposed scheme can also be used to communicate or store the watermarked image as erasure code, to reduce communication errors over a network, due to the use of FRAT.

14

Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

Zhou L., She J., Li C., Pan C.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 2

285--295

EN

This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.

15

A Signal Subspace Speech Enhancement Approach Based on Joint Low-Rank and Sparse Matrix Decomposition

Sun C., Xie J., Leng Y.

Archives of Acoustics

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2016

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Vol. 41, No. 2

245--254

EN

Subspace-based methods have been effectively used to estimate enhanced speech from noisy speech samples. In the traditional subspace approaches, a critical step is splitting of two invariant subspaces associated with signal and noise via subspace decomposition, which is often performed by singular-value decomposition or eigenvalue decomposition. However, these decomposition algorithms are highly sensitive to the presence of large corruptions, resulting in a large amount of residual noise within enhanced speech in low signal-to-noise ratio (SNR) situations. In this paper, a joint low-rank and sparse matrix decomposition (JLSMD) based subspace method is proposed for speech enhancement. In the proposed method, we firstly structure the corrupted data as a Toeplitz matrix and estimate its effective rank value for the underlying clean speech matrix. Then the subspace decomposition is performed by means of JLSMD, where the decomposed low-rank part corresponds to enhanced speech and the sparse part corresponds to noise signal, respectively. An extensive set of experiments have been carried out for both of white Gaussian noise and real-world noise. Experimental results show that the proposed method performs better than conventional methods in many types of strong noise conditions, in terms of yielding less residual noise and lower speech distortion.

16

Modulation-Mode and Power Assignment in SVD-Assisted Broadband MIMO Systems using Polynomial Matrix Factorization

Sandmann A., Ahrens A., Lochmann S.

Przegląd Elektrotechniczny

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2015

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R. 91, nr 4

10-13

EN

Singular-value decomposition (SVD)-based multiple-input multiple-output (MIMO) systems have attracted a lot of attention in the wireless community. However, applying SVD to frequency-selective MIMO channels results in unequally weighted single-input single-output (SISO) channels requiring complex resource allocation techniques for optimizing the channel performance. Therefore, a different approach utilizing polynomial matrix factorization for removing the MIMO interference is analyzed, outperforming conventional SVD-based MIMO systems in the analyzed channel scenario.

PL

Analizowano właściowści układu SVD (single value decomposition) w technologii MIMO w bezprzewodowym przesyłaniu informacji. Tego typu układy mają problemy z alokacją kanałów. Dlatego zaproponowano inny system wykorzystujący rozkład macierzy wielomianowej do usuwania interferencji kanałów.

17

A study of parallel techniques for dimensionality reduction and its impact on the quality of text processing algorithms

Pietroń M., Wielgosz M., Karwatowski M., Wiatr K.

Measurement Automation Monitoring

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2015

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Vol. 61, No. 7

352--353

EN

The presented algorithms employ the Vector Space Model (VSM) and its enhancements such as TFIDF (Term Frequency Inverse Document Frequency) with Singular Value Decomposition (SVD). TFIDF were applied to emphasize the important features of documents and SVD was used to reduce the analysis space. Consequently, a series of experiments were conducted. They revealed important properties of the algorithms and their accuracy. The accuracy of the algorithms was estimated in terms of their ability to match the human classification of the subject. For unsupervised algorithms the entropy was used as a quality evaluation measure. The combination of VSM, TFIDF, and SVD came out to be the best performing unsupervised algorithm with entropy of 0.16.

18

Using Singular Value Decomposition (SVD) as a solution for search result clustering

Abdulla H. D., Abdelrahman A. S., Snasel V.

Poznan University of Technology Academic Journals. Electrical Engineering

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2014

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No. 80

71--78

EN

There are many search engines in the web, but they return a long list of search results, ranked by their relevancies to the given query. Web users have to go through the list and examine the titles and (short) snippets sequentially to identify their required results. In this paper we present how usage of Singular Value Decomposition (SVD) as a very good solution for search results clustering. Results are presented by visualizing neural network. Neural network is responsive for reducing result dimension to two dimensional space and we are able to present result as a picture that we are able to analyze.

19

Hankel Singular Value Decomposition as a method of preprocessing the Magnetic Resonance Spectroscopy

Staniszewski M., Polański A.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 6

354--357

EN

The signal resulting from magnetic resonance spectroscopy is occupied by noises and irregularities so in the further analysis preprocessing techniques have to be introduced. The main idea of the paper is to develop a model of a signal as a sum of harmonics and to find its parameters. Such an approach is based on singular value decomposition applied to the data arranged in the Hankel matrix (HSVD) and can be used in each step of preprocessing techniques. For that purpose a method has was tested on real phantom data.

PL

Sygnał pochodzący z badania spektroskopii rezonansu magnetycznego zawiera również liczne szumy oraz nieprawidłości, stąd aby zastosować wyniki jako narzędzie diagnostyczne należy wprowadzić kilka usprawnień. W tym celu stosuje się filtrowanie, korekcję linii bazowej, korekcję fazy, korekcję prądów wirowych oraz usuwanie niechcianych komponentów, które nazywa się przetwarzaniem wstępnym. W dalszej analizie bardzo ważna jest identyfikacja poszczególnych metabolitów, którą można otrzymać poprzez zamodelowanie sygnału. Głównym pomysłem przedstawionym w artykule jest rozwinięcie modelu sygnału jako sumy harmonicznych. Metoda polega na znalezieniu parametrów opisujących sygnał takich jak amplituda, przesunięcie fazowe, częstotliwości i współczynnik tłumienia. Takie podejście bazuje na rozkładzie według wartości osobliwych (SVD) zastosowanym na danych zawartych w macierzy Hankela (HSVD), który dekomponuje sygnał na sumę harmonicznych oraz wylicza potrzebne parametry. Autor zaproponował zastosowanie HSVD w technikach przetwarzania wstępnego. Artykuł opisuje główne kroki przetwarzania i rozwiązanie każdej części oparte na HSVD. Podsumowując można stwierdzić, iż HSVD stosuje się w dekompozycji sygnału ale może być również skutecznym narzędziem w przetwarzaniu wstępnym. Artykuł składa się z 6 rozdziałów, w tym wstępu, rozdziału opisującego HSVD, metody przetwarzania wstępnego i główne wyniki, wniosków i referencji. W artykule znajdują się 4 obrazki oraz 7 referencji.

20

Comparison of five SVD-based algorithms for calibration of spectrophotometric analyzers

Wagner J., Morawski R. Z., Miękina A.

Metrology and Measurement Systems

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2014

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Vol. 21, nr 2

191--204

EN

Spectrophotometry is an analytical technique of increasing importance for the food industry, applied i.a. in the quantitative assessment of the composition of mixtures. Since the absorbance data acquired by means of a spectrophotometer are highly correlated, the problem of calibration of a spectrophotometric analyzer is, as a rule, numerically ill-conditioned, and advanced data-processing methods must be frequently applied to attain an acceptable level of measurement uncertainty. This paper contains a description of four algorithms for calibration of spectrophotometric analyzers, based on the singular value decomposition (SVD) of matrices, as well as the results of their comparison - in terms of measurement uncertainty and computational complexity - with a reference algorithm based on the estimator of ordinary least squares. The comparison is carried out using an extensive collection of semi-synthetic data representative of trinary mixtures of edible oils. The results of that comparison show the superiority of an algorithm of calibration based on the truncated SVD combined with a signal-to-noise ratio used as a criterion for the selection of regularisation parameters - with respect to other SVD-based algorithms of calibration.