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Additive white Gaussian noise

About: Additive white Gaussian noise is a(n) research topic. Over the lifetime, 15263 publication(s) have been published within this topic receiving 261193 citation(s). The topic is also known as: AWGN.

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Open accessJournal ArticleDOI: 10.1109/TIP.2017.2662206
Kai Zhang1, Wangmeng Zuo1, Yunjin Chen, Deyu Meng2  +1 moreInstitutions (3)
Abstract: The discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks, such as Gaussian denoising, single image super-resolution, and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.

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Topics: Video denoising (74%), Non-local means (69%), Basis pursuit denoising (63%) ...read more

3,742 Citations


Open accessJournal ArticleDOI: 10.1109/TIT.2008.926344
Abstract: For the fully connected K user wireless interference channel where the channel coefficients are time-varying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR)=K/2log(SNR)+o(log(SNR)) . Thus, the K user time-varying interference channel almost surely has K/2 degrees of freedom. Achievability is based on the idea of interference alignment. Examples are also provided of fully connected K user interference channels with constant (not time-varying) coefficients where the capacity is exactly achieved by interference alignment at all SNR values.

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Topics: Zero-forcing precoding (62%), Interference (communication) (55%), Channel capacity (54%) ...read more

3,299 Citations


Open accessBook
Andrew J. Viterbi1Institutions (1)
01 Jan 1995-
Abstract: 1. Introduction. Definition and Purpose. Basic Limitations of the Conventional Approach. Spread Spectrum Principles. Organization of the Book. 2. Random and Pseudorandom Signal Generation. Purpose. Pseudorandom Sequences. Maximal Length Linear Shift Register Sequences. Randomness Properties of MLSR Sequences. Conclusion. Generating Pseudorandom Signals (Pseudonoise) from Pseudorandom Sequences. First- and Second-Order Statistics of Demodulator Output in Multiple Access Interference. Statistics for QPSK Modulation by Pseudorandom Sequences. Examples. Bound for Bandlimited Spectrum. Error Probability for BPSK or QPSK with Constant Signals in Additive Gaussian Noise and Interference. Appendix 2A: Optimum Receiver Filter for Bandlimited Spectrum. 3. Synchronization of Pseudorandom Signals. Purpose. Acquisition of Pseudorandom Signal Timing. Hypothesis Testing for BPSK Spreading. Hypothesis Testing for QPSK Spreading. Effect of Frequency Error. Additional Degradation When N is Much Less Than One Period. Detection and False Alarm Probabilities. Fixed Signals in Gaussian Noise (L=1). Fixed Signals in Gaussian Noise with Postdetection Integration (L>1). Rayleigh Fading Signals (L>/=1). The Search Procedure and Acquisition Time. Single-Pass Serial Search (Simplified). Single-Pass Serial Search (Complete). Multiple Dwell Serial Search. Time Tracking of Pseudorandom Signals. Early-Late Gate Measurement Statistics. Time Tracking Loop. Carrier Synchronization. Appendix 3A: Likelihood Functions and Probability Expressions. Bayes and Neyman-Pearson Hypothesis Testing. Coherent Reception in Additive White Gaussian Noise. Noncoherent Reception in AWGN for Unfaded Signals. Noncoherent Reception of Multiple Independent Observations of Unfaded Signals in AWGN. Noncoherent Reception of Rayleigh-Faded Signals in AWGN. 4. Modulation and Demodulation of Spread Spectrum Signals in Multipath and Multiple Access Interference. Purpose. Chernoff and Battacharyya Bounds. Bounds for Gaussian Noise Channel. Chernoff Bound for Time-Synchronous Multiple Access Interference with BPSK Spreading. Chernoff Bound for Time-Synchronous Multiple Access Interference with QPSK Spreading. Improving the Chernoff Bound by a Factor of 2. Multipath Propagation: Signal Structure and Exploitation. Pilot-Aided Coherent Multipath Demodulation. Chernoff Bounds on Error Probability for Coherent Demodulation with Known Path Parameters. Rayleigh and Rician Fading Multipath Components. Noncoherent Reception. Quasi-optimum Noncoherent Multipath Reception for M-ary Orthogonal Modulation. Performance Bounds. Search Performance for Noncoherent Orthogonal M-ary Demodulators. Power Measurement and Control for Noncoherent Orthogonal M-ary Demodulators. Power Control Loop Performance. Power Control Implications. Appendix 4A: Chernoff Bound with Imperfect Parameter Estimates. 5. Coding and Interleaving. Purpose. Interleaving to Achieve Diversity. Forward Error Control Coding - Another Means to Exploit Redundancy. Convolutional Code Structure. Maximum Likelihood Decoder - Viterbi Algorithm. Generalization of the Preceding Example. Convolutional Code Performance Evaluation. Error Probability for Tailed-off Block. Bit Error Probability. Generalizations of Error Probability Computation. Catastrophic Codes. Generalization to Arbitrary Memoryless Channels - Coherent and Noncoherent. Error Bounds for Binary-Input, Output-Symmetric Channels with Integer Metrics. A Near-Optimal Class of Codes for Coherent Spread Spectrum Multiple Access. Implementation. Decoder Implementation. Generating Function and Performance. Performance Comparison and Applicability. Orthogonal Convolutional Codes for Noncoherent Demodulation of Rayleigh Fading Signals. Implementation. Performance for L-Path Rayleigh Fading. Conclusions and Caveats. Appendix 5A: Improved Bounds for Symmetric Memoryless Channels and the AWGN Channel. Appendix 5B: Upper Bound on Free Distance of Rate 1/n Convolutional Codes. 6. Capacity, Coverage, and Control of Spread Spectrum Multiple Access Networks. General. Reverse Link Power Control. Multiple Cell Pilot Tracking and Soft Handoff. Other-Cell Interference. Propagation Model. Single-Cell Reception - Hard Handoff. Soft Handoff Reception by the Better of the Two Nearest Cells. Soft Handoff Reception by the Best of Multiple Cells. Cell Coverage Issues with Hard and Soft Handoff. Hard Handoff. Soft Handoff. Erlang Capacity of Reverse Links. Erlang Capacity for Conventional Assigned-Slot Multiple Access. Spread Spectrum Multiple Access Outage - Single Cell and Perfect Power Control. Outage with Multiple-Cell Interference. Outage with Imperfect Power Control. An Approximate Explicit Formula for Capacity with Imperfect Power Control. Designing for Minimum Transmitted Power. Capacity Requirements for Initial Accesses. Erlang Capacity of Forward Links. Forward Link Power Allocation. Soft Handoff Impact on Forward Link. Orthogonal Signals for Same-Cell Users. Interference Reduction with Multisectored and Distributed Antennas. Interference Cancellation. Epilogue. References and Bibliography. Index.

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Topics: Pseudorandom noise (60%), Multipath propagation (58%), Chernoff bound (57%) ...read more

2,780 Citations


Journal ArticleDOI: 10.1109/TIT.2010.2043769
Abstract: This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ? isclosely approximated by C - ?(V/n) Q-1(?) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion , and Q is the complementary Gaussian cumulative distribution function.

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Topics: Channel capacity (58%), Decoding methods (52%), Cumulative distribution function (51%) ...read more

2,408 Citations


Open accessJournal ArticleDOI: 10.1109/TIP.2003.818640
Abstract: We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.

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  • Fig. 6. Comparison of denoising results onBarbara image (cropped to 150 150 for visibility of the artifacts). From left to right and top to bottom: Original image; Noisy image ( = 25, PSNR = 20:2 dB); Results of Liet al. [35] (PSNR = 28:2 dB); Our method (PSNR = 29:1 dB).
    Fig. 6. Comparison of denoising results onBarbara image (cropped to 150 150 for visibility of the artifacts). From left to right and top to bottom: Original image; Noisy image ( = 25, PSNR = 20:2 dB); Results of Liet al. [35] (PSNR = 28:2 dB); Our method (PSNR = 29:1 dB).
  • Fig. 1. Comparison of coefficient statistics from an example image subband (a vertical subband of theBoats image, left panels) with those arising from simulation of a local GSM model (right panels). Model parameters (covariance matrix and the multiplier prior density) are estimated by maximizing the likelihood of the observed set of wavelet coefficients. (a,b) Log marginal histograms. (c,d) Conditional histograms of two spatially adjacent coefficients. Brightness corresponds to probability, except that each column has been independently rescaled to fill the range of display intensities.
    Fig. 1. Comparison of coefficient statistics from an example image subband (a vertical subband of theBoats image, left panels) with those arising from simulation of a local GSM model (right panels). Model parameters (covariance matrix and the multiplier prior density) are estimated by maximizing the likelihood of the observed set of wavelet coefficients. (a,b) Log marginal histograms. (c,d) Conditional histograms of two spatially adjacent coefficients. Brightness corresponds to probability, except that each column has been independently rescaled to fill the range of display intensities.
  • TABLE I DENOISING PERFORMANCE EXPRESSED ASPEAK SIGNAL-TO-NOISE RATIO, 20 log (255= ) IN DB, WHERE IS THE ERROR STANDARD DEVIATION. EVERY ENTRY IS THE AVERAGE USING EIGHT DIFFERENT NOISE SAMPLES. LAST COLUMN SHOWS THE ESTIMATED STANDARD DEVIATION OF THESERESULTS FOREACH NOISE LEVEL
    TABLE I DENOISING PERFORMANCE EXPRESSED ASPEAK SIGNAL-TO-NOISE RATIO, 20 log (255= ) IN DB, WHERE IS THE ERROR STANDARD DEVIATION. EVERY ENTRY IS THE AVERAGE USING EIGHT DIFFERENT NOISE SAMPLES. LAST COLUMN SHOWS THE ESTIMATED STANDARD DEVIATION OF THESERESULTS FOREACH NOISE LEVEL
  • Fig. 2. Nonlinear estimation functions resulting from restriction of our method to smaller neighborhoods. (a) Neighborhood of size one (reference coefficient only) and (b) neighborhood of size two (reference coefficient plus parent).
    Fig. 2. Nonlinear estimation functions resulting from restriction of our method to smaller neighborhoods. (a) Neighborhood of size one (reference coefficient only) and (b) neighborhood of size two (reference coefficient plus parent).
  • Fig. 5. Comparison of denoising performance of several recently published methods. Curves depict output PSNR as a function of input PSNR. Square symbols indicate our results, taken from Table I. (a,b) circles [32]; crosses [35]; asterisk [52]3; (c,d) crosses [31]; diamonds [51].
    Fig. 5. Comparison of denoising performance of several recently published methods. Curves depict output PSNR as a function of input PSNR. Square symbols indicate our results, taken from Table I. (a,b) circles [32]; crosses [35]; asterisk [52]3; (c,d) crosses [31]; diamonds [51].
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Topics: Mean squared error (57%), Additive white Gaussian noise (56%), Estimation theory (54%) ...read more

2,342 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20228
2021373
2020467
2019598
2018520
2017574

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Topic's top 5 most impactful authors

Shlomo Shamai

59 papers, 1.8K citations

Norman C. Beaulieu

28 papers, 512 citations

Mohamed-Slim Alouini

19 papers, 742 citations

Alex Stephenne

16 papers, 268 citations

Sergio Verdu

16 papers, 6.6K citations

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