The Cramer–Rao lower bound in a non-AWGN model for the affine phase retrieval

2021 ◽  
pp. 2050089
Author(s):  
Zhitao Zhuang ◽  
Kaixin Wang
Keyword(s):  
Lower Bound ◽  
Mean Square Error ◽  
Gaussian Noise ◽  
Phase Retrieval ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Mean Square ◽  
Cramer Rao Lower Bound ◽  
The Difference

In this paper, we derive the Cramer–Rao lower bound (CRLB) in a non-additive white Gaussian noise (AWGN) model for the affine phase retrieval (APR) and simulate the difference of CRLB and mean square error produced by PhaseLift of phase retrieval and APR in AWGN and non-AWGN cases.

scholarly journals On the achievable rate of bandlimited continuous-time AWGN channels with 1-bit output quantization

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sandra Bender ◽  
Meik Dörpinghaus ◽  
Gerhard P. Fettweis
Keyword(s):  
Lower Bound ◽  
Mutual Information ◽  
Gaussian Noise ◽  
Continuous Time ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Information Rate ◽  
Achievable Rate ◽  
Zero Crossing ◽  
Lower Bounding

AbstractWe consider a real continuous-time bandlimited additive white Gaussian noise channel with 1-bit output quantization. On such a channel the information is carried by the temporal distances of the zero-crossings of the transmit signal. We derive an approximate lower bound on the capacity by lower-bounding the mutual information rate for input signals with exponentially distributed zero-crossing distances, sine-shaped transition waveform, and an average power constraint. The focus is on the behavior in the mid-to-high signal-to-noise ratio (SNR) regime above 10 dB. For hard bandlimited channels, the lower bound on the mutual information rate saturates with the SNR growing to infinity. For a given SNR the loss with respect to the unquantized additive white Gaussian noise channel solely depends on the ratio of channel bandwidth and the rate parameter of the exponential distribution. We complement those findings with an approximate upper bound on the mutual information rate for the specific signaling scheme. We show that both bounds are close in the SNR domain of approximately 10–20 dB.

scholarly journals Robust Gaussian Noise Detection and Removal in Color Images using Modified Fuzzy Set Filter

2020 ◽  
Vol 30 (1) ◽  
pp. 240-257
Author(s):  
Akula Suneetha ◽  
E. Srinivasa Reddy
Keyword(s):  
Image Quality ◽  
Mean Square Error ◽  
Fuzzy Set ◽  
Digital Image ◽  
Gaussian Noise ◽  
Digital Images ◽  
Structural Similarity ◽  
Fuzzy Rules ◽  
Mean Square ◽  
Image Edges

Abstract In the data collection phase, the digital images are captured using sensors that often contaminated by noise (undesired random signal). In digital image processing task, enhancing the image quality and reducing the noise is a central process. Image denoising effectively preserves the image edges to a higher extend in the flat regions. Several adaptive filters (median filter, Gaussian filter, fuzzy filter, etc.) have been utilized to improve the smoothness of digital image, but these filters failed to preserve the image edges while removing noise. In this paper, a modified fuzzy set filter has been proposed to eliminate noise for restoring the digital image. Usually in fuzzy set filter, sixteen fuzzy rules are generated to find the noisy pixels in the digital image. In modified fuzzy set filter, a set of twenty-four fuzzy rules are generated with additional four pixel locations for determining the noisy pixels in the digital image. The additional eight fuzzy rules ease the process of finding the image pixels,whether it required averaging or not. In this scenario, the input digital images were collected from the underwater photography fish dataset. The efficiency of the modified fuzzy set filter was evaluated by varying degrees of Gaussian noise (0.01, 0.03, and 0.1 levels of Gaussian noise). For performance evaluation, Structural Similarity (SSIM), Mean Structural Similarity (MSSIM), Mean Square Error (MSE), Normalized Mean Square Error (NMSE), Universal Image Quality Index (UIQI), Peak Signal to Noise Ratio (PSNR), and Visual Information Fidelity (VIF) were used. The experimental results showed that the modified fuzzy set filter improved PSNR value up to 2-3 dB, MSSIM up to 0.12-0.03, and NMSE value up to 0.38-0.1 compared to the traditional filtering techniques.

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