Iterative Algorithm for Parameterization of Two-Region Piecewise Uniform Quantizer for the Laplacian Source

Motivated by the fact that uniform quantization is not suitable for signals having non-uniform probability density functions (pdfs), as the Laplacian pdf is, in this paper we have divided the support region of the quantizer into two disjunctive regions and utilized the simplest uniform quantization with equal bit-rates within both regions. In particular, we assumed a narrow central granular region (CGR) covering the peak of the Laplacian pdf and a wider peripheral granular region (PGR) where the pdf is predominantly tailed. We performed optimization of the widths of CGR and PGR via distortion optimization per border–clipping threshold scaling ratio which resulted in an iterative formula enabling the parametrization of our piecewise uniform quantizer (PWUQ). For medium and high bit-rates, we demonstrated the convenience of our PWUQ over the uniform quantizer, paying special attention to the case where 99.99% of the signal amplitudes belong to the support region or clipping region. We believe that the resulting formulas for PWUQ design and performance assessment are greatly beneficial in neural networks where weights and activations are typically modelled by the Laplacian distribution, and where uniform quantization is commonly used to decrease memory footprint.

Symmetric Quantile Quantizer Parameterization for the Laplacian Source: Qualification for Contemporary Quantization Solutions

In this paper, we consider the opportunities and constraints, which rest on quantization as a guiding principle for data representation and compression. In particular, we propose a novel model of Symmetric Quantile Quantizer (SQQ) and we describe in detail its parameterization. We suggest a simple method for offline precalculation of its parameters and we examine the inevitable loss of information introduced by SQQ, as an important part of bit optimization task at the traditional network level, which can be globally mapped out in many contemporary solutions. Our anticipation is that such precalculated values can be leveraged in deterministic quantization process. We highlight that this notice heavily relies on the fact that the values of interest are distributed according to the Laplacian distribution, which we consider in the paper. The basic difference of our SQQ and the previously established asymptotically optimal quantizer model, that is, Scalar Companding Quantizer (SCQ), is reflected in the fact that, in SCQ model, both decision thresholds and representation levels are determined in accordance with the specified compressor function, whereas in our SQQ model, a precedence of SCQ model for the straightforward decision thresholds calculation is used, while the representation levels are optimally determined for the specified decision thresholds and assumed Laplacian distribution. As a result, our SQQ outperforms SCQ in terms of signal-to-quantization noise ratio (SQNR). As stated in this paper, there are numerous indications to make us believe that appropriate quantizer parameterization will move us closer to an optimization in the amount of the transferred data in bits, which is strongly dependent on the amount of SQNR.

Modelling of Random Selfish Behavior Attack using Single Sided Laplacian Distribution and Performance Evaluation for High Security Communications in Mobile Ad-hoc Networks

Background: The performance of Mobile Ad-hoc Networks get severely degraded due to various attacks including Selfish Behaviour attack. The detection of malicious nodes and avoidance of such nodes for data forwarding is important to enhance the MANET’s performance. Methods: A probabilistic model based on Single Sided Laplacian distribution for the random ON/OFF switching time of this attack is proposed. The model is used to make appropriate decisions regarding assignment of trust levels to suspicious nodes. The proposed protocol, based on this trust along with Confidence values of nodes, referred to as OLSRT-C protocol is used to select the optimum path for data forwarding. Simulations are carried out using Network Simulator NS2.35. Results: The random behavior of Selfish Behaviour attack is analyzed by considering all the possible random parameters. The random deployment of mobile nodes, number of malicious nodes, number of times the malicious nodes switch and timing instances at which these nodes change their states are considered. From the results, it is observed that, the OLSRTC protocol gives stable performance for Packet Delivery Ratio and Routing Overheads whereas for OLSR protocol, Packet Delivery Ratio gradually reduces and Routing Overheads increase, for percentage of malicious nodes increase from 10% to 50%. For OLSRT-C protocol, Average Energy Consumption per node increases marginally compared to OLSR protocol. Conclusion: The proposed OLSRT-C protocol successfully mitigates randomized Selfish Behaviour attack with marginal increase in the Average Energy Consumption per node. The Protocol Efficacy for OLSRT-C protocol is much higher compared to OLSR protocol.

Improving TDWZ Correlation Noise Estimation: A Deep Learning based Approach

Transform domain Wyner-Ziv video coding (TDWZ) has shown its benefits in compressing video applications with limited resources such as visual surveillance systems, remote sensing and wireless sensor networks. In TDWZ, the correlation noise model (CNM) plays a vital role since it directly affects to the number of bits needed to send from the encoder and thus the overall TDWZ compression performance. To achieve CNM with high accurate for TDWZ, we propose in this paper a novel CNM estimation approach in which the CNM with Laplacian distribution is adaptively estimated based on a deep learning (DL) mechanism. The proposed DL based CNM includes two hidden layers and a linear activation function to adaptively update the Laplacian parameter. Experimental results showed that the proposed TDWZ codec significantly outperforms the relevant benchmarks, notably by around 35% bitrate saving when compared to the DISCOVER codec and around 22% bitrate saving when compared to the HEVC Intra benchmark while providing a similar perceptual quality.

An Entropy-Based Algorithm with Nonlocal Residual Learning for Image Compressive Sensing Recovery

Image recovery from compressive sensing (CS) measurement data, especially noisy data has always been challenging due to its implicit ill-posed nature, thus, to seek a domain where a signal can exhibit a high degree of sparsity and to design an effective algorithm have drawn increasingly more attention. Among various sparsity-based models, structured or group sparsity often leads to more powerful signal reconstruction techniques. In this paper, we propose a novel entropy-based algorithm for CS recovery to enhance image sparsity through learning the group sparsity of residual. To reduce the residual of similar packed patches, the group sparsity of residual is described by a Laplacian scale mixture (LSM) model, therefore, each singular value of the residual of similar packed patches is modeled as a Laplacian distribution with a variable scale parameter, to exploit the benefits of high-order dependency among sparse coefficients. Due to the latent variables, the maximum a posteriori (MAP) estimation of the sparse coefficients cannot be obtained, thus, we design a loss function for expectation–maximization (EM) method based on relative entropy. In the frame of EM iteration, the sparse coefficients can be estimated with the denoising-based approximate message passing (D-AMP) algorithm. Experimental results have shown that the proposed algorithm can significantly outperform existing CS techniques for image recovery.