Noise Models for Ill-Posed Problems

2015 ◽  
pp. 1-24
Author(s):  
Paul N. Eggermont ◽  
Vincent LaRiccia ◽  
M. Zuhair Nashed
Keyword(s):  
Ill Posed ◽  
Noise Models

Noise Models for Ill-Posed Problems

2013 ◽  
pp. 1-24
Author(s):  
Paul N. Eggermont ◽  
Vincent LaRiccia ◽  
M. Zuhair Nashed
Keyword(s):  
Ill Posed ◽  
Noise Models

Noise Models for Ill-Posed Problems

2010 ◽  
pp. 739-762
Author(s):  
Paul N. Eggermont ◽  
Vincent LaRiccia ◽  
M. Zuhair Nashed
Keyword(s):  
Ill Posed ◽  
Noise Models

Noise Models for Ill-Posed Problems

2015 ◽  
pp. 1633-1658 ◽  
Author(s):  
Paul N. Eggermont ◽  
Vincent LaRiccia ◽  
M. Zuhair Nashed
Keyword(s):  
Ill Posed ◽  
Noise Models

Information and estimation in image processing

1987 ◽  
Vol 45 ◽  
pp. 14-17
Author(s):  
B. Roy Frieden
Keyword(s):  
Image Processing ◽  
Optical System ◽  
Large Amplitude ◽  
Communication Theory ◽  
Image Data ◽  
Direct Approach ◽  
Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

Quantum noise models for semiconductor lasers: is there a missing noise source?

1997 ◽  
Vol 44 (10) ◽  
pp. 1929-1936 ◽  
Author(s):  
A. BRAMATI, V. JOST, F. MARIN and E. G
Keyword(s):  
Semiconductor Lasers ◽  
Quantum Noise ◽  
Noise Source ◽  
Noise Models

Methods of solving ill-posed inverse problems

1983 ◽  
Vol 45 (5) ◽  
pp. 1237-1245 ◽  
Author(s):  
O. M. Alifanov
Keyword(s):  
Inverse Problems ◽  
Ill Posed

scholarly journals 1/f Noise Modelling and Characterization for CMOS Quanta Image Sensors

Sensors ◽  
2019 ◽  
Vol 19 (24) ◽  
pp. 5459
Author(s):  
Wei Deng ◽  
Eric R. Fossum
Keyword(s):  
Analog Circuits ◽  
Image Sensor ◽  
Image Sensors ◽  
Correlated Double Sampling ◽  
Cmos Image Sensors ◽  
Source Follower ◽  
Cmos Analog Circuits ◽  
Different Origins ◽  
Noise Models ◽  
Fitting Model

This work fits the measured in-pixel source-follower noise in a CMOS Quanta Image Sensor (QIS) prototype chip using physics-based 1/f noise models, rather than the widely-used fitting model for analog designers. This paper discusses the different origins of 1/f noise in QIS devices and includes correlated double sampling (CDS). The modelling results based on the Hooge mobility fluctuation, which uses one adjustable parameter, match the experimental measurements, including the variation in noise from room temperature to –70 °C. This work provides useful information for the implementation of QIS in scientific applications and suggests that even lower read noise is attainable by further cooling and may be applicable to other CMOS analog circuits and CMOS image sensors.

scholarly journals A Nonlinearly Ill-Posed Problem of Reconstructing the Temperature from Interior Data

2008 ◽  
Vol 29 (3-4) ◽  
pp. 445-469
Author(s):  
Pham Hoang Quan ◽  
Dang Duc Trong ◽  
Alain Pham Ngoc Dinh
Keyword(s):  
Interior Data ◽  
Ill Posed

scholarly journals Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

2021 ◽  
Author(s):  
Radu Boţ ◽  
Guozhi Dong ◽  
Peter Elbau ◽  
Otmar Scherzer
Keyword(s):  
Linear Operator ◽  
Operator Equation ◽  
Convex Analysis ◽  
Convergence Rates ◽  
Linear Operator Equation ◽  
Optimal Convergence Rates ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Given ◽  
Theoretical Results

AbstractRecently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

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