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All Journal Jurnal Matematika Sains dan Teknologi MATHunesa: Jurnal Ilmiah Matematika
Zaqiyatus Shahadah
Universitas Billfath
Agriculture, Biological Sciences & Forestry Mathematics Other

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The Application of Dicrete Wavelet Transform for Digital Image Compression Ahmad Khairul Umam; Pukky Tetralian Bantining Ngastiti; Aris Alfan; Zaqiyatus Shahadah; Amanda Fatma Muamalah
Jurnal Matematika Sains dan Teknologi Vol. 25 No. 1 (2024)
Publisher : LPPM Universitas Terbuka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33830/jmst.v25i1.3955.2024

Abstract

This article explains Discrete Wavelet Transform (DWT) in image compression. Wavelet transform is a generalization of Fourier transform, consisting of discrete and continuous wavelet transform. DWT has many uses, including image compression, fingerprint recognition, and image denoising. This research aims to know the steps of digital image compression using DWT and compare the original and resulting images. Efforts of DWT in digital image compression go by DWT's process, determining the threshold, sorting the absolute value of the image whether it is minor or more significant (equal to) threshold value, then is processed, Inverse Discrete Wavelet Transform (IDWT). This research explains the Peak Signal-to-Noise Ratio (PSNR), computing time, and compression ratio for three examples: the image of the cameraman, Lena, and a cat. The results determine that the highest PSNR values are wavelet of coiflets 3 for the cameraman, biorthogonal 3.5 for Lena, and coiflets 3 for the cat. The fastest computation times are wavelet of symlets 4 for the cameraman, symlets 4, coiflets 3 for Lena, and Daubechies 4 for the cat. Then, the highest compression ratios are wavelet of symlets 4, biorthogonal 3.5, coiflets 3 for the cameraman, Haar for Lena, and symlets 4, biorthogonal 3.5 for the cat. The results of this research are we get steps of the discrete wavelet transform for digital image compression. Also, we obtain types of wavelets with the highest PSNR values, the fastest computation times, and the highest compression ratios.
TRANSFORMASI WAVELET DISKRIT UNTUK DENOISING CITRA Ahmad Khairul Umam; Pukky Tetralian Bantining Ngastiti; Aris Alfan; Zaqiyatus Shahadah; Amanda Fatma Muamalah
MATHunesa: Jurnal Ilmiah Matematika Vol. 12 No. 02 (2024)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v12n2.p374-380

Abstract

Nowadays, topic of wavelet has many applications including image denoising. Wavelet Transform is divided into discrete wavelet transform and continuous wavelet transform. Besides for image denoising, it can also useful for image compression and others. In this research is discussed about steps image denoising using wavelet. Wavelets that used are Haar, Daubechies, biorthogonal, symlets and coiflets wavelets for hard thresholding and soft thresholding. Program is made according to steps/algorithm that were created. Then, we compare original image and result of image denoising. In this research, we use grayscale test image Lena and cat with size pixels. We use peak signal to noise ratio (PSNR) to measure performance of the algorithm. We also compare computational time.
KAJIAN TEOREMA TITIK TETAP DI RUANG B-METRIK YANG DIPERPANJANG Ahmad Khairul Umam; Aris Alfan; Ahmad Isro'il; Zaqiyatus Shahadah; Amanda Fatma Muamalah
MATHunesa: Jurnal Ilmiah Matematika Vol. 12 No. 02 (2024)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

This research gives more explaination in proof of theorem. The theorem is about existence and uniqueness a point is called fixed point in an extended b-metric space. Beside that, also we give example about extended b-metric space.
Co-Authors Ahmad Isro'il Ahmad Khairul Umam Amanda Fatma Muamalah Aris Alfan Pukky Tetralian Bantining Ngastiti