Total variation with automatic hyper-parameter estimation

The additive white Gaussian noise (AWGN) model is commonly used in the development of communication systems, and adequately models many noisy environments. However the impulsive noise from snapping shrimp is poorly approximated by this model. The mismatch in model has an adverse impact on the performance of conventional communication systems operating in warm shallow waters. The AWGN model may be replaced by the more general additive white symmetric α-stable noise (AWSαSN) model, which better approximates the heavy tailed noise due to snapping shrimp. When converted to the complex baseband representation, the resulting noise for the AWSαSN case is radically different from its Gaussian counterpart. In this talk some properties of baseband noise for the general AWSαSN case are investigated. These properties can be used to guide design decisions for coherent communication systems operating in warm shallow waters. The baseband noise is generally not isotropic and furthermore the real and imaginary components may be dependent. By varying certain physical parameters different non-isotropic distributions may be attained. The resulting properties can be exploited to design communication systems that are able to provide robust performance in the presence of snapping shrimp noise.

Multiplicative noise is often present in medical and biological imaging, such as magnetic resonance imaging (MRI), Ultrasound, positron emission tomography (PET), single photon emission computed tomography (SPECT), and fluorescence microscopy. Noise reduction in medical images is a difficult task in which linear filtering algorithms usually fail. Bayesian algorithms have been used with success but they are time consuming and computationally demanding. In addition, the increasing importance of the 3-D and 4-D medical image analysis in medical diagnosis procedures increases the amount of data that must be efficiently processed. This paper presents a Bayesian denoising algorithm which copes with additive white Gaussian and multiplicative noise described by Poisson and Rayleigh distributions. The algorithm is based on the maximum a posteriori (MAP) criterion, and edge preserving priors which avoid the distortion of relevant anatomical details. The main contribution of the paper is the unification of a set of Bayesian denoising algorithms for additive and multiplicative noise using a well-known mathematical framework, the Sylvester-Lyapunov equation, developed in the context of the Control theory.

Upper and lower bounds on the capacity and minimum energy-per-bit for general additive white Gaussian noise (AWGN) and frequency-division AWGN (FD-AWGN) relay channel models are established. First, the max-flow min-cut bound and the generalized block-Markov coding scheme are used to derive upper and lower bounds on capacity. These bounds are never tight for the general AWGN model and are tight only under certain conditions for the FD-AWGN model. Two coding schemes that do not require the relay to decode any part of the message are then investigated. First, it is shown that the "side-information coding scheme" can outperform the block-Markov coding scheme. It is also shown that the achievable rate of the side-information coding scheme can be improved via time sharing. In the second scheme, the relaying functions are restricted to be linear. The problem is reduced to a "single-letter" nonconvex optimization problem for the FD-AWGN model. The paper also establishes a relationship between the minimum energy-per-bit and capacity of the AWGN relay channel. This relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy-per-bit that do not differ by more than a factor of 1.45 for the FD-AWGN relay channel model and 1.7 for the general AWGN model.

Localization of sensor node is imperative in Wireless Sensor Networks (WSN) as data gathered at the user end become meaningless without location information of the node. In this work, impact of anchor position errors on WSN localization using Mobile Anchor Positioning (MAP) Algorithm has been investigated by evaluating two deployment strategies. In deployment I sensor nodes are randomly spread in the entire chosen area (1000 χ 1000) whilst deployment II has nodes spread in the central region of the chosen area. Firstly, MAP Algorithm employing three anchor nodes is investigated for the two deployments. To study the impact of mobile anchors on MAP, anchor number is increased to four and the two deployments are investigated again. Further, this work also investigates the effect of anchor position errors on localization accuracy of sensor nodes. Error term is modelled using Additive White Gaussian Noise (AWGN) Model. Performance metrices considered for validation are Average Root Mean Square Error and Execution time.

The capacity limits of fiber-optic communication systems in the nonlinear regime are not yet well understood. In this paper, we study the capacity of amplitude modulated first-order soliton transmission, defined as the maximum of the so-called time-scaled mutual information. Such definition allows us to directly incorporate the dependence of soliton pulse width to its amplitude into capacity formulation. The commonly used memoryless channel model based on noncentral chi-squared distribution is initially considered. Applying a variance normalizing transform, this channel is approximated by a unit-variance additive white Gaussian noise (AWGN) model. Based on a numerical capacity analysis of the approximated AWGN channel, a general form of capacity-approaching input distributions is determined. These optimal distributions are discrete comprising a mass point at zero (off symbol) and a finite number of mass points almost uniformly distributed away from zero. Using this general form of input distributions, a novel closed-form approximation of the capacity is determined showing a good match to numerical results. Finally, mismatch capacity bounds are developed based on split-step simulations of the nonlinear Schrdinger equation considering both single soliton and soliton sequence transmissions. This relaxes the initial assumption of memoryless channel to show the impact of both inter-soliton interaction and Gordon–Haus effects. Our results show that the inter-soliton interaction effect becomes increasingly significant at higher soliton amplitudes and would be the dominant impairment compared to the timing jitter induced by the Gordon–Haus effect.

We propose an enhanced log-likelihood ratio (E-LLR) technique for soft-decision forward error correction (SD-FEC) in intensity-modulation direct-detection (IMDD) systems with optical amplifiers and demonstrate its effectiveness in 7-core weakly coupled fiber transmission. In amplified IMDD, square-law photodetection and modulator nonlinearities cause amplified spontaneous emission noise to produce non-Gaussian signal statistics, invalidating conventional LLR assumptions and degrading SD-FEC performance. To address this issue, we abandon the classic additive white Gaussian noise (AWGN) model and introduce a channel model based on multi-parameter chi-square distributions that more accurately reflect optical channel noise. Unlike previous Gaussian and chi-square approaches, E-LLR uses a training sequence to estimate the variance and non-centrality parameters for each pulse-amplitude modulation (PAM) level, generating <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> distinct noncentral chi-square distributions for precise LLR computation in FEC decoding. Experimental results show that the proposed approach improves the receiver sensitivity by 1.13dB and reduces the decoding iterations of FEC compared with AWGN-model based schemes. These improvements contribute to reduced system complexity and decoding latency, while still achieving the required bit error rate threshold.

Generalized signal-dependent noise model and parameter estimation for natural images

An analysis of performance of Serially Concatenated Convolutional Codes (SCCC) is evaluated on Additive White Gaussian Noise model channel, which is used as a basis, and actions of SCCC on Raleigh flat slow and flat fast faded channels are evaluated in this research work. In DCS the SCCC are utilized to reduce the bit error rates. SCCC encoder consists of RSCC. The major thrust is iterative decoding. This research has utilized BCJR and TDA decoding algorithms. This research analyzed SCCC with interleaved scheme. The BPSK modulation was considered. Performance metric for SCCC over Memory less AWGN channel, and memory based channels i.e. Rayleigh slow and fast Faded Channel is BER verses SNR.

In this paper, the error performance of the tag-to-reader link of a passive UHF (Electronic Product Code - EPC - Generation 2) RFID system is examined. An error-correcting technique is introduced that is based on the cyclic redundancy check (CRC) bits transmitted by the tag with backscatter biphase-M (or FM0) modulation. The proposed technique uses a look-up table that allows the correction of single errors in the received EPC. Numerical results, using additive white Gaussian noise (AWGN) and flat Rayleigh fading channel models, show that a better performance is obtained, in the sense of either reducing the error rate or increasing the distance between tag and reader.

Addresses the problem of speech recognition with signals corrupted by additive noise at moderate signal-to-noise ratio (SNR). A model for additive noise is presented and used to compute the uncertainty about the hidden clean signal so as to weight the estimation provided by spectral subtraction. Weighted dynamic time warping (DTW) and Viterbi (HMM) algorithms are tested, and the results show that weighting the information along the signal can substantially increase the performance of spectral subtraction, an easily implemented technique, even with a poor estimation for noise and without using any information about the speaker. It is also shown that the weighting procedure can reduce the error rate when cepstral mean normalization is also used to cancel the convolutional noise.

We consider the additive white Gaussian noise (AWGN) cognitive fading interference channel consisting of one primary and multiple secondary transmitter-receiver pairs. The secondary transmitters have non-causal knowledge of the primary message. We find a tuple of achievable rates by utilizing the discrete superposition model (DSM), which is a simplified, deterministic channel model. The coding scheme devised for the DSM can be translated into a coding scheme for the AWGN model, where the rate achieved in the AWGN model is at most a constant gap below the rate achieved in the DSM. We then calculate the average throughput of the secondary pairs under the assumption of Rayleigh fading channels. The main result is that our scheme performs well in the weak interference regime. The sum-throughput increases with the number of secondary pairs.

Recently, there has been a great deal of work developing super-resolution reconstruction (SRR) algorithms. While many such algorithms have been proposed, the almost SRR estimations are based on L1 or L2 statistical norm estimation, therefore these SRR algorithms are usually very sensitive to their assumed noise model that limits their utility. The real noise models that corrupt the measure sequence are unknown; consequently, SRR algorithm using L1 or L2 norm may degrade the image sequence rather than enhance it. Therefore, the robust norm applicable to several noise and data models is desired in SRR algorithms. This paper first comprehensively reviews the SRR algorithms in this last decade and addresses their shortcomings, and latter proposes a novel robust SRR algorithm that can be applied on several noise models. The proposed SRR algorithm is based on the stochastic regularization technique of Bayesian MAP estimation by minimizing a cost function. For removing outliers in the data, the Lorentzian error norm is used for measuring the difference between the projected estimate of the high-resolution image and each low-resolution image. Moreover, Tikhonov regularization and Lorentzian-Tikhonov regularization are used to remove artifacts from the final answer and improve the rate of convergence. The experimental results confirm the effectiveness of our method and demonstrate its superiority to other super-resolution methods based on L1 and L2 norms for several noise models such as noiseless, additive white Gaussian noise (AWGN), poisson noise, salt and pepper noise, and speckle noise.

There are two major routes to address inverse problems in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities embody models of both the distribution of the unknown variables and their statistical dependence with respect to the observed data. Estimation typically relies on the minimization of an expected loss (e.g. minimum mean squared error, or MMSE). The second route designs (often convex) optimization problems involving the sum of a data fidelity term and a penalty term promoting certain types of unknowns (e.g., sparsity, using an ℓ 1 penalty). Well known relations between these two approaches have led to some widely spread misconceptions. In particular, while the so-called Maximum A Posteriori (MAP) estimate with a Gaussian noise model does lead to an optimization problem with a quadratic data-fidelity term, we disprove through explicit examples the common belief that the converse would be true. It was shown [7] , [9] that for denoising in the presence of additive Gaussian noise, for any prior probability on the unknowns, MMSE estimation can be expressed as a penalized least squares problem, with the apparent characteristics of a MAP estimate with Gaussian noise and a (generally) different prior on the unknowns. In other words, the second route is rich enough to build all possible MMSE estimators associated to additive Gaussian noise via a well chosen penalty. We generalize these results beyond Gaussian denoising and characterize noise models for which the same phenomenon occurs. In particular, we prove that with (a variant of) Poisson noise and any prior probability on the unknowns, MMSE estimation can again be expressed as the solution of a penalized least squares optimization problem. For additive scalar denoising the phenomenon holds if and only if the noise distribution is log-concave. In particular, Laplacian denoising can (perhaps surprisingly) be expressed as the solution of a penalized least squares problem. In the multivariate case, the same phenomenon occurs when the noise model belongs to a particular subset of the exponential family. For multivariate additive denoising, the phenomenon holds if and only if the noise is white and Gaussian.

Orthogonal Frequency Division Multiplexing (OFDM) is an extensively used transmission technique that enables feasible modulation and demodulation in communication systems.Channel Estimation (CE) is applied in channel conditions where time-varying features are essential.However, Inter-Symbol Interference (ISI) occurs in MOFDM and leads to inaccurate channel impulse response estimation due to multi-path propagation.Therefore, this research proposes a Rayleigh Distribution with Flower Pollination Algorithm (RDFPA) for pilot insertion in CE to reduce Normalized Mean Square Error (NMSE) in the OFDM system.Additionally, the RDFPA identifies optimal factors by exploring possible areas in the global search space with quick convergence.To encode and decode the signals, the Space-Time Block Code (STBC) is applied, which improves communication and enhances the signal's spatial diversity.The 16-quadrate Amplitude Modulation (16-QAM) is used for signal modulation and demodulation.The Additive White Gaussian Noise (AWGN) is applied to the transfer signal from the transmitter to the receiver.The Bit Error Rate (BER), NMSE, and Symbol Error Rate (SER) are used to evaluate the RDFPA performance in CE.The RDFPA achieved a lower NMSE of 0.510-1 for a Signal-to-Noise Ratio (SNR) of 10dB, which is better than the existing Tunicate Swarm Optimization (TSO).

Intravascular elastography is an emerging imaging technique that maps the strain distribution. The strain within the arterial wall is caused by the pulsatile mechanical solicitation of the blood pressure during cardiac cycle. In contrary to other elastographic applications, the transducer is positioned in the lumen and not in direct contact with the tissue. Therefore, segmentation of the luminal contour is required. Numerous contour detection techniques have been developed, but their automated character is generally strongly limited by either the initialization of parameters, or the manual selection of the contour search area. The segmentation method, presented in this paper, is fully automated and still accurate. This technique is based on active contours and exploits the property that, if ultrasound image textures can be modeled by Rayleigh distributions, two different regions can be identified by two different Rayleigh parameters. The contour is thus searched as a continuous smooth closed curve, that separates optimally, in the sense of the maximum a posteriori (MAP) approach, two Rayleigh distributions, one representing the blood, the other the arterial tissue. Unfortunately the luminal border corresponds rarely to the global maximum position of the likelihood function, but rather to the position of a local maximum. Indeed the arterial wall is heterogeneous, resulting in a brightness in ultrasound images, modeled by more than one Rayleigh distribution. For these reasons, an adaptive and iterative process of contour search area reduction has been introduced, based on energy criteria. Coronary artery images from 16 patients, acquired with a 20 MHz ultrasound scanner were analyzed using the developed method. Resulting automated contours show a strong correlation with those manually drawn by two experienced observers.