Image Reconstruction Using Zernike Moment and Discrete Cosine Transform: A Comparison

Transform coding has been the focus of the research for image compression. In previous research, the Amplitude and Group Partitioning (AGP) coding scheme is proved to be a low complexity algorithm with higher performance, clearly one of the state-of-art transform coding techniques. However, the previous AGP is used along with the Discrete Cosine Transform (DCT) and the discrete wavelet transform. In this paper, a different transform, the Lapped Orthogonal Transform (LOT), replaces the DCT in conjunction with the AGP. This is the first time LOT and AGP have been combined in a coding method. The definition and design of the LOT are discussed. An objective metric to measure the performance of transform, coding gain, is calculated for both the DCT and the LOT. The LOT has slightly higher coding gain than the DCT. The principles of the LOT based AGP image codec (LOT-AGP) are presented and a complete codec, encoder and decoder, is implemented in software. The performance of the LOT-AGP is compared with other block transform coding schemes: the baseline JPEG codec and the DCT based AGP image codec (DCT- AGP) by both objective evaluation and subjective evaluation. The Peak Signal to Noise Ratio (PSNR) is calculated for these three coding schemes. The two AGP codecs are much better than the JPEG codec on PSNR, from about 1.7 dB to 3 dB depending on bit rate. The two AGP schemes have PSNR differences only to a small degree. Visually, the LOT-AGP has the best-reconstructed images among these three at all bit rates. In addition, the coding results of two other state-of-art progressive image codecs are cited for further comparison. One is the Set Partitioning in Hierarchical Trees (SPIHT) algorithm with a dyadic wavelet transform, and the other is Tran and Nguyen's method with the generalized LOT transform. The AGP coding and the adaptive Huffman entropy coding of LOT-AGP are less complex and the memory usage is smaller than in these two progressive codecs. Comparing these three codecs, i.e. the LOT-AGP and the two progressive codecs in PSNR small only small differences in PSNR. SPIHT has about 1 dB higher PSNR than the LOT-AGP and Tran and Nguyen's method for the test image Lena. For the test image Barbara, the PSNR of the LOT- AGP is about 0.5 dB higher than that of the SPIHT and 0.5 dB lower than that of Tran and Nguyen's method. This low- complexity and high performance codec may provide a new direction for the implementation of image compression.

The success of internet technology transform the world of technology and fashioned our life such a lot easier. The matter of duplication and unauthorized use of information become a great threat within the field of technology. To beat these problems, techniques like digital watermarking, steganography and cryptography were introduced. The approach of embedding a secret data associated with the digital signal inside the signal itself is digital watermarking. For embedding and detecting the watermark different techniques are used; spatial domain techniques like Least Significant Bit (LSB) and Patch Work Algorithm, then the frequency domain techniques such as Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) and Discrete Fourier Transform (DFT) are some of them. Combination of DCT & DWT technique for digital watermarking is proposed here. The proposed methodology is implemented in MATLAB 2017a simulator and result is analysed using evaluation parameters like Peak Signal to Noise Ratio (PSNR) & Mean Square Error (MSE). PSNR value obtained for the case of watermarking using DWT is 27.46 and MSE value is 17.45. The value of PSNR for watermarking using DCT is 41.4 and for MSE the value is 0.67. The PSNR and MSE values obtained for watermarking using LSB technique is 50.55 and 0.58. The proposed method improves the watermarked image quality and the MSE & PSNR value obtained is 0.52 and 51.017 respectively.

In the paper “An analog 2-D DCT processor,” authors have presented a row-column method for computing 2-D discrete cosine transform (DCT). They have reported minimum peak signal-to-noise ratios (PSNR) 40.6 dB and 31.4 dB for 4-point and 8-point DCT, respectively. The main objective of this comment letter is to point out that those PSNR values are not correctly calculated. The actual minimum PSNR values are shown to be 24.7 dB and 22.7 dB for 4-point and 8-point DCT, respectively. Similarly, maximum PSNR values are corrected in this letter.

There are many invisible image watermarking techniques that can be used to provide authenticity and intellectual property rights. This paper presents a comprehensive frame work of invisible image watermarking techniques FFT (Fast Fourier Transform), DCT (Discrete Cosine Transform) and DWT (Discrete Wavelet Transform) based on Arnold Transform (AT) scrambling. DWT based on Arnold Transform gives better results in terms of authenticity and robustness as compared to FFT and DCT technique. The performance of each invisible image watermarking technique is theoretically and mathematically analyzed based on parameter PSNR (Peak Signal to Noise Ratio) and MSE (Mean Square Error). Also, the performance of each technique is analyzed on different noise and transformation attack. An experiment based on gray scale image that shows there is consistency between the theoretical analysis and the experimental result analysis. In extraction process, invisible image watermarking technique is applied on both host image and watermarked image.

With the growth of new technologies, usage of internet and world wide web, it is becoming imperative day by day to protect the digital data from various kinds of unauthorized attacks. It has become mandatory to provide copyright protection to the digital data. In this work a new and hybrid algorithm is proposed to provide better security to the digital image. A watermark image is added into the original image using the concept of Discrete Cosine Transformation (DCT), Singular Value Decomposition (SVD) and artificial neural network. PSNR (Peak signal to noise ratio) value is used to analyze the results.

Analysis of noise sensitivity of Tchebichef and Zernike moments with application to image watermarking

Prior research studies have shown that the peak signal to noise ratio (PSNR) is the most frequent watermarked image quality metric that is used for determining the levels of strength and weakness of watermarking algorithms. Conversely, normalised cross correlation (NCC) is the most common metric used after attacks were applied to a watermarked image to verify the strength of the algorithm used. Many researchers have used these approaches to evaluate their algorithms. These strategies have been used for a long time, however, which unfortunately limits the value of PSNR and NCC in reflecting the strength and weakness of the watermarking algorithms. This paper considers this issue to determine the threshold values of these two parameters in reflecting the amount of strength and weakness of the watermarking algorithms. We used our novel watermarking technique for embedding four watermarks in intermediate significant bits (ISB) of six image files one-by-one through replacing the image pixels with new pixels and, at the same time, keeping the new pixels very close to the original pixels. This approach gains an improved robustness based on the PSNR and NCC values that were gathered. A neural network model was built that uses the image quality metrics (PSNR and NCC) values obtained from the watermarking of six grey-scale images that use ISB as the desired output and that are trained for each watermarked image’s PSNR and NCC. The neural network predicts the watermarked image’s PSNR together with NCC after the attacks when a portion of the output of the same or different types of image quality metrics (PSNR and NCC) are obtained. The results indicate that the NCC metric fluctuates before the PSNR values deteriorate.

Information system security is a crucial aspect in the digital era, especially for protecting sensitive data. One method to enhance data security is steganography, a technique for concealing information within digital media. This study analyzes the effectiveness of the Discrete Cosine Transform (DCT) method in digital image steganography. The research follows several stages, including literature review, system design, DCT implementation using MATLAB/Python, and performance evaluation based on Peak Signal-to-Noise Ratio (PSNR), Mean Squared Error (MSE), and Normalized Correlation (NC). Experimental results indicate that the DCT method achieves a high PSNR value (averaging above 40 dB) and a low MSE value, ensuring minimal image distortion after data embedding. Compared to the Least Significant Bit (LSB) method, DCT provides better resistance to visual analysis and is more suitable for images with transform-based compressions, such as JPEG. This study concludes that the DCT method is an effective steganography technique for enhancing information system security, despite challenges related to computational complexity and data embedding capacity. Future research may explore hybrid methods that combine DCT with other techniques to improve efficiency and robustness against various steganographic analysis attacks.

A comparative analysis of image steganography based on DCT algorithm and steganography tool to hide nuclear reactors confidential information

One of the main contributions of this paper is to show that contrary to the common belief Tchebichef moments are more sensitive to noise added to the image than Zernike moments. We show this by imposing different types and levels of noise on various images and measuring the error due to the added noise alone after image reconstruction. To calculate the error due to added noise alone, the image reconstruction error is subtracted from the total error, which initially includes both reconstruction and added noise errors. Another contribution of this paper is to present some analysis and compare the reconstruction capability of Tchebichef moments to that of Zernike and Legendre moments in noise free environments independent of the image used. We show this by spectrally analyzing the performance of Tchebichef, Legendre, and Zernike moments using single frequency images. Here the total reconstruction error of an arbitrary image is equal to the integration of the spectral errors, whose transfer functions are calculated using single frequency images, for all frequencies.

Steganography is the process of embedding data into a media form such as image, voice, and video. The major methods used for data hiding are the frequency domain and the spatial domain. In the frequency domain, the secret data bits are inserted into the coefficients of the image pixel's frequency representation such as Discrete Cosine Transform (DCT) , Discrete Fourier Transform (DFT) and Discrete Wavelet Transform (DWT) . On the other hand, in the spatial domain method, the secret data bits are inserted directly into the images' pixels value decomposition. The Lest Significant Bit (LSB) is consider as the most widely spatial domain method used for data hiding. LSB embeds the secret message's bits into the least significant bit plane( Binary decomposition) of the image in a sequentially manner . The LSB is simple, but it poses some critical issues. The secret message is easily detected and attacked duo to the sequential embedding process. Moreover, embedding using a higher bit plane would degrade the image quality. In this paper, we are proposing a novel data hiding method based on Lucas number system. We use Lucas number system to decompose the images' pixels values to allow using higher bit plane for embedding without degrading the image's quality. The experimental results show that the proposed method achieves better Peak Signal to Noise Ratio ( PSNR) than the LSB method for both gray scale and color images. Moreover, the security of the hidden data is enhanced by using Pseudo Random Number Generators(PRNG) for selecting the secret data bits to be embedded and the image's pixels used for embedding.

As an orthogonal moment, Zernike moment (ZM) is an attractive image feature in a number of application scenarios due to its distinguishing properties. However, we find that for digital images, the commonly used Cartesian method for ZM computation has compromised the advantages of ZMs because of their non-ideal accuracy stemming from two inherent sources of errors, i.e., the geometric error and the integral error. There exists considerable errors in image reconstruction using ZMs calculated with the Cartesian method. In this paper, we propose a polar coordinate based algorithm for the computation of ZMs, which avoids the two kinds of errors and greatly improves the accuracy of ZM computation. We present solutions to the key issues in ZM computation under polar coordinate system, including the derivation of computation formulas, the polar pixel arrangement scheme, and the interpolation-based image conversion etc. As a result, ZM-based image reconstruction can be performed much more accurately.

Energy compaction property of the Discrete Cosine Transform (DCT) leads its usage in image and video compression applications. Nowadays power consumption is the major problem in modern multimedia applications. Hence circuit complexity and area reduction are the optimal ways for the power consumption reduction. In this paper the proposed DCTs represented as approximate DCT-Case I, II and III are constructed with basis elements Ci = {0, ±1, ±2}. Proposed Approximate DCT Case I and II have been derived from 16 × 16 point DCT rounding off operation and odd row sign replacement. Approximate DCT Case III has been derived based on (Potluri et al. in Meas Sci Technol 23(11):1–15, 2012). Peak signal to noise ratio (PSNR), total error energy and computational complexity wise approximate DCT Case III improved when compared to (Potluri et al. in Meas Sci Technol 23(11):1–15, 2012). Proposed approximate DCT Case I, II and III 8 × 8 matrixes satisfy the orthogonal property through a quantization process.

WITHDRAWN: Contrasting the performance metrics of discrete transformations on digital image steganography using artificial intelligence

In recent years most of researcher’s has done tremendous work in the field of medical image applications such as Magnetic Resonance Imaging (MRI), Ultra Sound, CT scan but still there are many research and experiments in medical imaging field and diagnosing of human health by Health Care Institutes. There is a growing interest for medical imaging de-noising as a hot area of research and also imaging equipment as a device. It is used for better image processing and highlighting the important features. These images are affected with random noise during acquisition, analyzing and Transmission process. This results in blurry image visible in low contrast. Wavelet transforms have effective method to separate the noise from the original medical image by using threshold techniques without affecting the important data of an image. Wavelet transform enables us to use the forward wavelet transform to represent sub-band of the original image in decomposition process then reconstructing this sub band coefficients to original image using inverse wavelet transform. In this work, the quality of medical image has been evaluated using filter assessment parameters like Variance, standard deviation, the squared difference error between original medical image & de-noised image (MSE) and the ratio between original image & noisy image. From numerical results, we can see that the algorithm is efficient de-noising of noisy medical image. When, investigating with Baye’s threshold techniques it achieved the Best value of peak signal to noise ratio (PSNR). For best medical image de-noising, the wavelet based de-noising algorithm has been investigated and results of Baye’s techniques and hard & soft threshold methods have been compared.