Image extraction using convolution kernal

This paper discusses about the noise reduction of images using the convolution matrix. The convolution kernel matrix filters generate new features of the input images with good quality.The noise reduction methods based on convolution kernel is achieved by deep learning theory along with the difference equations. The random variation of the colour and brightness are taken as authenticated coefficients of the images. Convolution techniques along withrecurrent neuralnetwork are applied into theinput image. This input image is divided into the matrix of pixel values. The optimal enhanced image is arrived through convolution kernel using computational learning of autonomous difference equations.

On the Generalization of the Random Projection Method for Problems of the Recovery of Object Signal Described by Models of Convolution Type

Introduction. In technical systems, there is a common situation when transformation input-output is described by the integral equation of convolution type. This situation accurses if the object signal is recovered by the results of remote measurements. For example, in spectrometric tasks, for an image deblurring, etc. Matrices of the discrete representation for the output signal and the kernel of convolution are known. We need to find a matrix of the discrete representation of a signal of the object. The well known approach for solving this problem includes the next steps. First, the kernel matrix has to be represented as the Kroneker product. Second, the input-output transformation has to be presented with the usage of Kroneker product matrices. Third, the matrix of the discrete representation of the object has to be found. The object signal matrix estimation obtained with the help of pseudo inverting of Kroneker decomposition matrices is unstable. The instability of the object signal estimation in the case of usage of Kroneker decomposition matrices is caused by their discrete ill posed matrix properties (condition number is big and the series of the singular numbers smoothly decrease to zero). To find solutions of discrete ill-posed problems we developed methods based on the random projection and the random projection with an averaging by the random matrices. These methods provide a stable solutions with a small computational complexity. We consider the problem of object signals recovering in the systems where an input-output transformation is described by the integral equation of a convolution. To find a solution for these problems we need to build a generalization for two-dimensional signals case of the random projection method. Purpose. To develop a stable method of the recovery of object signal for the case in which an input-output transformation is described by the integral equation of a convolution. Results and conclusions. We developed the method of a stable recovery of object signal for the case in which an input-output transformation is described by the integral equation of a convolution. The stable estimation of the object signal is provided by Kroneker decomposition of the kernel matrix of convolution, computation of random projections for Kroneker factorization matrices, and a selection of the optimal dimension of a projector matrix. The method is illustrated by its application in technical problems.

Numerical simulation of squeezing Cu–Water nanofluid flow by a kernel-based method

The main aim of this paper is to propose a kernel-based method for solving the problem of squeezing Cu–Water nanofluid flow between parallel disks. Our method is based on Gaussian Hilbert–Schmidt SVD (HS-SVD), which gives an alternate basis for the data-dependent subspace of “native” Hilbert space without ever forming kernel matrix. The well-conditioning linear system is one of the critical advantages of using the alternate basis obtained from HS-SVD. Numerical simulations are performed to illustrate the efficiency and applicability of the proposed method in the sense of accuracy. Numerical results obtained by the proposed method are assessed by comparing available results in references. The results demonstrate that the proposed method can be recommended as a good option to study the squeezing nanofluid flow in engineering problems.

SAR Image Change Detection Based on Multi-scale Feature Extraction

In order to improve the contrast of the difference image and reduce the interference of the speckle noise in the synthetic aperture radar (SAR) image, this paper proposes a SAR image change detection algorithm based on multi-scale feature extraction. In this paper, a kernel matrix with weights is used to extract features of two original images, and then the logarithmic ratio method is used to obtain the difference images of two images, and the change area of the images are extracted. Then, the different sizes of kernel matrix are used to extract the abstract features of different scales of the difference image. This operation can make the difference image have a higher contrast. Finally, the cumulative weighted average is obtained to obtain the final difference image, which can further suppress the speckle noise in the image.

Perbandingan Aplikasi Algoritma Kernel K-Means pada Graf Bipartit dan K-Means pada Matriks Dokumen- Istilah dalam Dataset Penelitian Covid-19 RISTEKBRIN

<p class="Abstrak">Merebaknya kasus Covid-19 di Indonesia telah memunculkan berbagai macam topik penelitian yang dilakukan oleh para peneliti di berbagai bidang dan dari bermacam institusi. Berdasarkan data yang dihimpun oleh portal Sinta Ristekbrin, terdapat 351 topik penelitian yang telah diunggah oleh para peneliti. Kajian ini dimaksudkan untuk menganalisis dan memetakan topik penelitian yang sedang dan/atau telah dilakukan selama kurun waktu terjadinya pandemi Covid-19 di tanah air. Analisis dan pemetaan dilakukan dengan menerapkan algoritma kernel <em>k-means</em> untuk klastering dokumen berbasis graf bipartit dan <em>k-mean</em>s pada matriks dokumen-istilah. Dataset penelitian Covid-19 Ristekbrin dimodelkan sebagai graf bipartit antara daftar istilah dengan dokumennya. Selanjutnya skor kemiripan dihitung dengan metode kernel. Nilai matriks kernel yang mencerminkan skor kemiripan antar dokumen digunakan sebagai masukan bagi algoritma klastering kernel <em>k-means</em> yang memberikan hasil berupa pemetaan topik penelitian. Sebagai pembanding, algoritma <em>k-means</em> diterapkan pada matriks dokumen-istilah untuk klastering topik penelitian Covid-19. Dari kedua metode tersebut, hasil klastering diuji dengan validasi internal menggunakan indeks Dunn. Indeks Dunn digunakan karena dalam dataset tidak tersedia informasi awal mengenai label atau nama dari masing-masing klaster. Hasil penelitian ini menunjukkan bahwa algoritma kernel <em>k-means</em> memberikan validasi yang sedikit lebih baik dibandingkan dengan <em>k-means</em>. Hasil kajian ini diharapkan dapat memberikan tambahan informasi yang mendukung program pemerintah dalam mempercepat penanganan Covid-19 di Indonesia.</p><p class="Abstrak"> </p><p class="Abstrak"><em><strong>Abstract</strong></em></p><p class="Abstract"><em>The outbreak concerning the Covid-19 case in Indonesia has raised various topics of research carried out by researchers in diverse fields and from many institutions. Based on data compiled by the Sinta Ristekbrin portal, 351 research topics have been uploaded by researchers. This study is aimed to analyze and map research topics that are being and/or have been conducted during the period of the Covid-19 pandemic in Indonesia. Analysis and mapping are accomplished by applying the kernel k-means algorithm for document clustering based on bipartite graphs and k-means on document term matrix. Ristekbrin's Covid-19 research dataset is modeled as a bipartite graph between terms and documents. Furthermore, the similarity score is calculated using the kernel method. The kernel matrix value that represents the similarity score between documents is used as input for the kernel k-means clustering algorithm, which provides the results of mapping research topics. As comparison, we applied original k-means algorithm on the document-term matrix of the dataset. From these two methods, the clustering results were validated using Dunn index as an internal validation. The Dunn index was used because the dataset did not provide initial information regarding the label or name of each clusters..The comparison Dunn index shows that the kernel k-means algorithm outperforms than the k-means algorithm. This study is expected to provide additional information that supports government programs in accelerating the handling of Covid-19 in Indonesia..</em></p><p class="Abstrak"><em><strong><br /></strong></em></p>