# Image compression using singular value decomposition

VIT University

^{1}01 Nov 2017-Vol. 263, Iss: 4, pp 042082

TL;DR: Goal here is to achieve the image compression while preserving the important features which describe the original image.

Abstract: We often need to transmit and store the images in many applications. Smaller the image, less is the cost associated with transmission and storage. So we often need to apply data compression techniques to reduce the storage space consumed by the image. One approach is to apply Singular Value Decomposition (SVD) on the image matrix. In this method, digital image is given to SVD. SVD refactors the given digital image into three matrices. Singular values are used to refactor the image and at the end of this process, image is represented with smaller set of values, hence reducing the storage space required by the image. Goal here is to achieve the image compression while preserving the important features which describe the original image. SVD can be adapted to any arbitrary, square, reversible and non-reversible matrix of m × n size. Compression ratio and Mean Square Error is used as performance metrics.

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TL;DR: The novelty of the proposed methodology is its architecture, which combines the acquisition of specialist knowledge and formalising and recording it in a useful form for new employees in the company.

Abstract: (1) Background: Improving the management and effectiveness of employees’ learning processes within manufacturing companies has attracted a high level of attention in recent years, especially within the context of Industry 4.0. Convolutional Neural Networks with a Support Vector Machine (CNN-SVM) can be applied in this business field, in order to generate workplace procedures. To overcome the problem of usefully acquiring and sharing specialist knowledge, we use CNN-SVM to examine features from video material concerning each work activity for further comparison with the instruction picture’s features. (2) Methods: This paper uses literature studies and a selected workplace procedure: repairing a solid and using a fuel boiler as the benchmark dataset, which contains 20 s of training and a test video, in order to provide a reference model of features for a workplace procedure. In this model, the method used is also known as Convolutional Neural Networks with Support Vector Machine. This method effectively determines features for the further comparison and detection of objects. (3) Results: The innovative model for generating a workplace procedure, using CNN-SVM architecture, once built, can then be used to provide a learning process to the employees of manufacturing companies. The novelty of the proposed methodology is its architecture, which combines the acquisition of specialist knowledge and formalising and recording it in a useful form for new employees in the company. Moreover, three new algorithms were created: an algorithm to match features, an algorithm to detect each activity in the workplace procedure, and an algorithm to generate an activity scenario. (4) Conclusions: The efficiency of the proposed methodology can be demonstrated on a dataset comprising a collection of workplace procedures, such as the repair of the solid fuel boiler. We also highlighted the impracticality for managers of manufacturing companies to support learning processes in a company, resulting from a lack of resources to teach new employees.

19 citations

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TL;DR: In this article, the authors used singular value decomposition to verify Altshuler and Shklovskii's prediction for disordered three-, four-, and five-dimensional single-electron Anderson models on square lattices in the metallic regime.

Abstract: Disordered quantum systems feature an energy scale known as the Thouless energy. For energy ranges below this scale, the properties of the energy spectrum can be described by random matrix theory. Above this scale a different behavior sets in. For a metallic system it was shown long ago by Altshuler and Shklovskii [Sov. Phys. JETP 64, 127 (1986)] that the number variance should increase as a power law with power dependent on only the dimensionality of the system. Although tantalizing hints at this behavior were seen in previous numerical studies, it is quite difficult to verify this prediction using the standard local unfolding methods. Here we use a different unfolding method, i.e., singular value decomposition, and establish a connection between the power law behavior of the scree plot (the singular values ranked by their amplitude) and the power law behavior of the number variance. Thus, we are able to numerically verify Altshuler and Shklovskii's prediction for disordered three-, four-, and five-dimensional single-electron Anderson models on square lattices in the metallic regime. The same method could be applied to systems such as the Sachdev-Ye-Kitaev model and various interacting many-body models for which the many-body localization occurs. It was recently reported that such systems exhibit a Thouless energy, and analyzing the spectrum's behavior on larger scales is of much current interest.

9 citations

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01 Nov 2020

TL;DR: In this paper, the authors compared two dimension reduction algorithms, namely Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) using K-Means clustering method to find out the best algorithm with the smallest Bouldin Davies Index evaluation.

Abstract: Clustering is a method of dividing datasets into several groups that have similarity or the same characteristics. High-dimensional Datasets will influence the effectiveness of the grouping process. This study compares two dimension reduction algorithms, namely Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) using K-Means clustering method to find out the best algorithm with the smallest Bouldin Davies Index evaluation. The dataset of this study involved public data from UCIMachine Learning which contains the number of weekly sales of a product. Data processing is performed by comparing the number of clusters from 3 to 10 and the dimension reduction from 2 to 10. From the data processing the RapidMiner tools, application with dimension reduction can provide better results than without dimension reduction. In particular, the PCA algorithm shows better results than the SVD, with which the best number of clusters is 5, and the number of dimensional reductions is 3 with a Bouldin Index of 0.376.

4 citations

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TL;DR: In this article , it was shown that the large scale energy spectrum of a canonical microscopical model featuring MBL, displays a non-universal behavior at intermediate scales, which is distinct from the deviation from universality seen in the single particle Anderson regime.

Abstract: In recent years it became clear that the metallic regime of systems that exhibit a many body localization (MBL) behavior show properties which are quite different than the vanilla metallic region of the single particle Anderson regime. Here we show that the large scale energy spectrum of a canonical microscopical model featuring MBL, displays a non-universal behavior at intermediate scales, which is distinct from the deviation from universality seen in the single particle Anderson regime. The crucial step in revealing this behavior is a global unfolding of the spectrum performed using the singular value decomposition (SVD) which takes into account the sample to sample fluctuations of the spectra. The spectrum properties may be observed directly in the singular value amplitudes via the scree plot, or by using the SVD to unfold the spectra and then perform a number of states variance calculation. Both methods reveal an intermediate scale of energies which follow super Posissonian statistics.

4 citations

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TL;DR: This research paper deals with the implementation of an image captioning algorithm using Tensorflow, Keras, and Python, as well as a way proposed for optimization, using image compression techniques, to minimize data size, execution time, and computer resources.

Abstract: This research paper deals with the implementation of an image captioning algorithm using Tensorflow, Keras, and Python, as well as a way proposed for optimization, using image compression techniques. The objective is to use image compression techniques to minimize data size, execution time, and computer resources since machine learning applications often have numerous constraints concerning energy consumption, processing power, and dataset sizes, thus making them less efficient for real-time, applied use cases. We can find new ways to apply machine learning in more simple real-life applications by attempting to reduce such obstacles.

##### References

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13 Dec 2007

TL;DR: SVD is utilized to compress and reduce the storage space of an image and the effect of rank in SVD decomposition is investigated to measure the quality in terms of MSE and PSNR.

Abstract: It is well known that the images, often used in variety of computer applications, are difficult to store and transmit. One possible solution to overcome this problem is to use a data compression technique where an image is viewed as a matrix and then the operations are performed on the matrix. Image compression is achieved by using Singular Value Decomposition (SVD) technique on the image matrix. The advantage of using the SVD is the property of energy compaction and its ability to adapt to the local statistical variations of an image. Further, the SVD can be performed on any arbitrary, square, reversible and non reversible matrix of m x n size. In this paper, SVD is utilized to compress and reduce the storage space of an image. In addition, the paper investigates the effect of rank in SVD decomposition to measure the quality in terms of MSE and PSNR.

64 citations

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21 Apr 1997TL;DR: This paper investigates a transform adaptation technique, applied to transform coding of images, as a way of exploiting the variation in local statistics within an image, using the relationship between the Karhunen-Loeve transform and singular value decomposition and their energy compaction properties.

Abstract: This paper investigates a transform adaptation technique, applied to transform coding of images, as a way of exploiting the variation in local statistics within an image. The method makes use of the relationship between the Karhunen-Loeve transform (KLT) and singular value decomposition (SVD), and their energy compaction properties. We compare this approach to a standard KLT coding system. Motivated by increased coding efficiency an analysis-by-synthesis approach using switching between the KLT coding system and the hybrid KLT-SVD system is proposed. The switching is implemented using a global rate-distortion criterion. The results are encouraging and the proposed techniques provide new insights on how to use SVD in an image compression system.

56 citations

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07 Nov 2005TL;DR: The purpose of this paper is to discuss the usage possibility of singular value decomposition in image compression applications and prove the usage feasibility of SVD-based image compression.

Abstract: The purpose of this paper is to discuss the usage possibility of singular value decomposition in image compression applications A mistake viewpoint that is about SVD-based image compression scheme is demonstrated The paper goes deep to study three schemes of SVD-based image compression and prove the usage feasibility of SVD-based image compression

43 citations

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25 Nov 2009

TL;DR: The SVD is utilized to compress and reduce the storage space of an image and the effect of rank in SVD decomposition is investigated to measure the quality in terms of Compression Ratio and PSNR.

Abstract: It is well known that the images, often used in variety of computer applications, are difficult to store and transmit. One possible solution to overcome this problem is to use a data compression technique where an image is viewed as a matrix and then the operations are performed on the matrix. In this paper, image compression is achieved by using Singular Value Decomposition (SVD) technique on the image matrix. The advantage of using the SVD is the property of energy compaction and its ability to adapt to the local statistical variations of an image. Further, the SVD can be performed on any arbitrary, square, reversible and non reversible matrix of m x n size. In this paper, SVD is utilized to compress and reduce the storage space of an image. In addition, the paper investigates the effect of rank in SVD decomposition to measure the quality in terms of Compression Ratio and PSNR.

19 citations

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23 Mar 2016TL;DR: The method of SVD has been applied to mid-level digital image processing and the performance evaluation parameters for image compression viz.

Abstract: Singular Value Decomposition (SVD) deals with the decomposition of general matrices which has proven to be useful for numerous applications in science and engineering disciplines. In this paper the method of SVD has been applied to mid-level digital image processing. SVD transforms a given matrix into three different matrices, which in other words, means refactoring the digital image into three matrices. Refactoring is achieved by using singular values, and the image is represented with a smaller set of values. The primary aim is to achieve image compression by using less storage space in the memory and simultaneously preserving the useful features of original image. The experiments with different singular values are performed and the performance evaluation parameters for image compression viz. Compression Ratio, Mean Square Error, PSNR and Compressed Bytes are calculated for each SVD coefficient. The implementation tool for the tests and experiments is MATLAB.

12 citations