Finding the parameters of a Bernoulli-Gaussian Model

<div><div><div><p>A transmission medium perturbed by an additive noise from which the estimated noise power is all information known, is better modeled as a Gaussian channel. Since the Gaussian channel is, according to Information Theory, the worst channel to transmit information through, this is the most pessimistic assumption. When noise samples are available though, choosing to model the transmission medium using a more sophisticated model pays off. The Bernoulli-Gaussian channel, would be one such a choice. Finding the three parameters that characterize the Bernoulli-Gaussian stochastic process which mathematically models the noise is a task of paramount importance. Many algorithms can be used to estimate the parameters of this model based on numerical methods. In the current work a closed form expression to estimate the model parameters is presented. All that is required besides the estimation of the power of Bernoulli-Gaussian process from the available noise samples is the estimation of two additional quantities: the expected value of the absolute value of the amplitude of the process—the first absolute moment—plus the third absolute moment, viz., the expected value of the third power of the absolute value of the process. An alternative option, often used for power line communication, is to model the transmission medium as a channel in which the noise is represented by a three parameter stochastic process called Middleton Class A. Other models (like generalized-Bernoulli-Gaussian, or Bernoulli- Gaussian with memory) might render a better medium model than the Bernoulli-Gaussian channel. Estimating the parameters of these processes is however a cumbersome task and, as we show in the current work, the rate harvested by using the simple, yet more sophisticated, Bernoulli-Gaussian channel is increased as compared to the, more pessimistic, Gaussian channel, allowing one thus to more closely approach the true capacity. The communication system design can be much improved if a well fit Bernoulli-Gaussian stochastic process is selected to model the true noise. The incorporation of the Bernoulli-Gaussian channel in the communication system model leads to a better design as corroborated by the computer simulation results presented.</p></div></div></div>

Finding the parameters of a Bernoulli-Gaussian Model

<div><div><div><p>A transmission medium perturbed by an additive noise from which the estimated noise power is all information known, is better modeled as a Gaussian channel. Since the Gaussian channel is, according to Information Theory, the worst channel to transmit information through, this is the most pessimistic assumption. When noise samples are available though, choosing to model the transmission medium using a more sophisticated model pays off. The Bernoulli-Gaussian channel, would be one such a choice. Finding the three parameters that characterize the Bernoulli-Gaussian stochastic process which mathematically models the noise is a task of paramount importance. Many algorithms can be used to estimate the parameters of this model based on numerical methods. In the current work a closed form expression to estimate the model parameters is presented. All that is required besides the estimation of the power of Bernoulli-Gaussian process from the available noise samples is the estimation of two additional quantities: the expected value of the absolute value of the amplitude of the process—the first absolute moment—plus the third absolute moment, viz., the expected value of the third power of the absolute value of the process. An alternative option, often used for power line communication, is to model the transmission medium as a channel in which the noise is represented by a three parameter stochastic process called Middleton Class A. Other models (like generalized-Bernoulli-Gaussian, or Bernoulli- Gaussian with memory) might render a better medium model than the Bernoulli-Gaussian channel. Estimating the parameters of these processes is however a cumbersome task and, as we show in the current work, the rate harvested by using the simple, yet more sophisticated, Bernoulli-Gaussian channel is increased as compared to the, more pessimistic, Gaussian channel, allowing one thus to more closely approach the true capacity. The communication system design can be much improved if a well fit Bernoulli-Gaussian stochastic process is selected to model the true noise. The incorporation of the Bernoulli-Gaussian channel in the communication system model leads to a better design as corroborated by the computer simulation results presented.</p></div></div></div>

Development of Scalable Coding of Encrypted Images Using Modified Absolute Moment Block Truncation Code

Many researchers worked on scalable coding for unencrypted images, and there is more space for research in scalable coding for encrypted images. This paper proposes a novel method of scalable coding for encrypted images, especially for lossy compression images using the Modified Absolute Moment Block Truncation Code (MAMBTC) technique. The given input image is compressed using MAMBTC and then encrypted using a Pseudo-Random Number (PRNG) at the encryption phase. The PRNG is shared between the encoder and the decoder. At the decryption phase, the compressed pixel value is obtained by decryption using the PRNG and then reconstructed using MAMBTC, scaled by scaling factor 2 and Bilinear Interpolation Technique to obtain the original image. MAMBTC gives better image quality than Block Truncation Code (BTC), a higher PSNR of 36.32 dB, and a Compression ratio of 1.09, which makes the proposed system ready for the signal processing community/applications.

A High Fidelity Authentication Scheme for AMBTC Compressed Image Using Reference Table Encoding

In this paper, we propose a high-quality image authentication method based on absolute moment block truncation coding (AMBTC) compressed images. The existing AMBTC authentication methods may not be able to detect certain malicious tampering due to the way that the authentication codes are generated. In addition, these methods also suffer from their embedding technique, which limits the improvement of marked image quality. In our method, each block is classified as either a smooth block or a complex one based on its smoothness. To enhance the image quality, we toggle bits in bitmap of smooth block to generate a set of authentication codes. The pixel pair matching (PPM) technique is used to embed the code that causes the least error into the quantization values. To reduce the computation cost, we only use the original and flipped bitmaps to generate authentication codes for complex blocks, and select the one that causes the least error for embedment. The experimental results show that the proposed method not only obtains higher marked image quality but also achieves better detection performance compared with prior works.

Efficient Reversible Data Hiding Scheme for AMBTC-Compressed Images

Reversible data hiding has attracted significant attention from researchers because it can extract an embedded secret message correctly and recover a cover image without distortion. In this paper, a novel, efficient reversible data hiding scheme is proposed for absolute moment block truncation code (AMBTC) compressed images. The proposed scheme is based on the high correlation of neighboring values in two mean tables of AMBTC-compressed images to further losslessly encode these values and create free space for containing a secret message. Experimental results demonstrated that the proposed scheme obtained a high embedding capacity and guaranteed the same PSNRs as the traditional AMBTC algorithm. In addition, the proposed scheme achieved a higher embedding capacity and higher efficiency rate than those of some previous schemes while maintaining an acceptable bit rate.

Data Hiding Method for Color AMBTC Compressed Images Using Color Difference

Image compression technology and copyright protection are certainly the important technologies for free exchange of multimedia. For compression of an image, we propose a color Absolute Moment Block Trucation Coding (AMBTC) method using a common bit-plane created by k-means. In addition, a data hiding method based on a color AMBTC using Optimal Pixel Adjustment Process (OPAP) was proposed for copyright protection and confidential secret communication. The number of quantization levels of the proposed color AMBTC is nine per block. Therefore, the edge of the compressed color image can be expressed more delicately. As a result of the simulation, it can be seen that the edge of the image of the color AMBTC is close to the original image. Moreover, the data hiding performance of the proposed method also obtained excellent results. For the experiment, we measured the quality of the image using the Color Difference (CD) we proposed, and the measurement result was very satisfactory.

Pixel P Air-Wise Fragile Image Watermarking Based on HC-Based Absolute Moment Block Truncation Coding

In this paper, we first designed Huffman code (HC)-based absolute moment block truncation coding (AMBTC). Then, we applied Huffman code (HC)-based absolute moment block truncation coding (AMBTC) to design a pixel pair-wise fragile image watermarking method. Pixel pair-wise tampering detection and content recovery mechanisms were collaboratively applied in the proposed scheme to enhance readability even when images have been tampered with. Representative features are derived from our proposed HC-based AMBTC compression codes of the original image, and then serve as authentication code and recovery information at the same time during tamper detection and recovery operations. Recovery information is embedded into two LSB of the original image with a turtle shell-based data hiding method and a pre-determined matrix. Therefore, each non-overlapping pixel-pair carries four bits of recovery information. When the recipient suspects that the received image may have been tampered with, the compressed image can be used to locate tampered pixels, and then the recovery information can be used to restore the tampered pixels.

Self-Embedding Fragile Watermarking Scheme to Detect Image Tampering Using AMBTC and OPAP Approaches

Research on self-embedding watermarks is being actively conducted to solve personal privacy and copyright problems by image attack. In this paper, we propose a self-embedded watermarking technique based on Absolute Moment Block Truncation Coding (AMBTC) for reconstructing tampered images by cropping attacks and forgery. AMBTC is suitable as a recovery bit (watermark) for the tampered image. This is because AMBTC has excellent compression performance and image quality. Moreover, to improve the quality of the marked image, the Optimal Pixel Adjustment Process (OPAP) method is used in the process of hiding AMBTC in the cover image. To find a damaged block in a marked image, the authentication data along with the watermark must be hidden in the block. We employ a checksum for authentication. The watermark is embedded in the pixels of the cover image using 3LSB and 2LSB, and the checksum is hidden in the LSB. Through the recovering procedure, it is possible to recover the original marked image from the tampered marked image. In addition, when the tampering ratio was 45%, the image (Lena) could be recovered at 36 dB. The proposed self-embedding method was verified through an experiment, and the result was the recovered image showed superior perceptual quality compared to the previous methods.