On continuous image models and image analysis in the presence of correlated noise

1990 ◽  
Vol 22 (2) ◽  
pp. 332-349 ◽  
Author(s):  
Peter Hall ◽  
Inge Koch
Keyword(s):  
Image Processing ◽  
Image Analysis ◽  
Point Spread Function ◽  
Convergence Rates ◽  
Discrete Distributions ◽  
Correlated Noise ◽  
Point Spread ◽  
Special Cases ◽  
Spread Function ◽  
Image Models

Most theoretical studies of image processing employ discrete image models. While that might be a good approximation to digital analysis, it severely restricts the class of tractable models for the blur component of image degradation, and concentrates excessive attention on specialized features of the pixel lattice. It is analogous to modelling all real statistical data using discrete distributions, which is clearly unnecessary. In this paper we study a continuous model for image analysis, in the presence of systematic degradation via a point spread function and stochastic degradation by a second-order stationary random field. Thus, we depart from the restrictive white-noise models which are commonly used in the theory of image analysis. We establish a general result which describes the performance of optimal image processing methods when the noise process has short-range dependence. Concise limits to resolution are derived, depending on image type, point spread function and noise correlation. These results are developed in important special cases, giving explicit formulae for optimal smoothing sets and convergence rates.

On continuous image models and image analysis in the presence of correlated noise

1990 ◽  
Vol 22 (02) ◽  
pp. 332-349
Author(s):  
Peter Hall ◽  
Inge Koch
Keyword(s):  
Image Processing ◽  
Image Analysis ◽  
Point Spread Function ◽  
Convergence Rates ◽  
Discrete Distributions ◽  
Correlated Noise ◽  
Point Spread ◽  
Special Cases ◽  
Spread Function ◽  
Image Models

Most theoretical studies of image processing employ discrete image models. While that might be a good approximation to digital analysis, it severely restricts the class of tractable models for the blur component of image degradation, and concentrates excessive attention on specialized features of the pixel lattice. It is analogous to modelling all real statistical data using discrete distributions, which is clearly unnecessary. In this paper we study a continuous model for image analysis, in the presence of systematic degradation via a point spread function and stochastic degradation by a second-order stationary random field. Thus, we depart from the restrictive white-noise models which are commonly used in the theory of image analysis. We establish a general result which describes the performance of optimal image processing methods when the noise process has short-range dependence. Concise limits to resolution are derived, depending on image type, point spread function and noise correlation. These results are developed in important special cases, giving explicit formulae for optimal smoothing sets and convergence rates.

Millimeter wave image processing through point spread function engineering

2011 ◽  
Author(s):  
Joseph N. Mait ◽  
Richard D. Martin ◽  
Christopher A. Schuetz ◽  
Dennis W. Prather
Keyword(s):  
Image Processing ◽  
Millimeter Wave ◽  
Point Spread Function ◽  
Point Spread ◽  
Spread Function ◽  
Point Spread Function Engineering ◽  
Wave Image

scholarly journals Application of Blind Deconvolution Algorithm for Deblurring of Saturated Images

2019 ◽  
Vol 8 (2S3) ◽  
pp. 1383-1386
Keyword(s):  
Image Processing ◽  
Image Restoration ◽  
Point Spread Function ◽  
Blind Deconvolution ◽  
Visual Quality ◽  
Visual Examination ◽  
Point Spread ◽  
Spread Function ◽  
Sharp Image ◽  
Deblurring And Denoising

Image Restoration is a field of Image Processing which manages recuperating a unique and sharp image from a debased image utilizing a numerical corruption and reclamation model. This investigation centers around rebuilding of corrupted images which have been obscured by known or obscure debasement work. Image rebuilding which reestablishes an unmistakable image from a solitary haze image is a troublesome issue of assessing two questions: a point spread function (PSF) and its optimal image. Image deblurring can improve visual quality and mitigates movement obscure for dynamic visual examination. We propose a strategy to deblur immersed images for dynamic visual examination by applying obscure piece estimation and deconvolution demonstrating. The haze portion is assessed in a change space, though the deconvolution model is decoupled into deblurring and denoising stages by means of variable part

scholarly journals Profiler – A Fast and Versatile New Program for Decomposing Galaxy Light Profiles

2016 ◽  
Vol 33 ◽  
Author(s):  
Bogdan C. Ciambur
Keyword(s):  
Point Spread Function ◽  
Elliptical Galaxy ◽  
Exponential Model ◽  
Point Spread ◽  
Special Cases ◽  
Spread Function ◽  
Total Light ◽  
Elliptical Models ◽  
User Friendly ◽  
Light Profiles

AbstractI introduce Profiler, a user-friendly program designed to analyse the radial surface brightness profiles of galaxies. With an intuitive graphical user interface, Profiler can accurately model galaxies of a broad range of morphological types, with various parametric functions routinely employed in the field (Sérsic, core-Sérsic, exponential, Gaussian, Moffat, and Ferrers). In addition to these, Profiler can employ the broken exponential model for disc truncations or anti–truncations, and two special cases of the edge-on disc model: along the disc's major or minor axis. The convolution of (circular or elliptical) models with the point spread function is performed in 2D, and offers a choice between Gaussian, Moffat or a user-provided profile for the point spread function. Profiler is optimised to work with galaxy light profiles obtained from isophotal measurements, which allow for radial gradients in the geometric parameters of the isophotes, and are thus often better at capturing the total light than 2D image-fitting programs. Additionally, the 1D approach is generally less computationally expensive and more stable. I demonstrate Profiler's features by decomposing three case-study galaxies: the cored elliptical galaxy NGC 3348, the nucleated dwarf Seyfert I galaxy Pox 52, and NGC 2549, a double-barred galaxy with an edge-on, truncated disc.Profiler is freely available at https://github.com/BogdanCiambur/PROFILER.

On the amount of detail that can be recovered from a degraded signal

1987 ◽  
Vol 19 (2) ◽  
pp. 371-395 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Image Processing ◽  
Digital Image Processing ◽  
Digital Image ◽  
Point Spread Function ◽  
Test Pattern ◽  
Upper Bounds ◽  
Noisy Signal ◽  
Information Theoretic ◽  
Point Spread ◽  
Spread Function

Motivated by applications in digital image processing, we discuss information-theoretic bounds to the amount of detail that can be recovered from a defocused, noisy signal. Mathematical models are constructed for test-pattern, defocusing and noise. Using these models, upper bounds are derived for the amount of detail that can be recovered from the degraded signal, using any method of image restoration. The bounds are used to assess the performance of the class of linear restorative procedures. Certain members of the class are shown to be optimal, in the sense that they attain the bounds, while others are shown to be sub-optimal. The effect of smoothness of point-spread function on the amount of resolvable detail is discussed concisely.

On the amount of detail that can be recovered from a degraded signal

1987 ◽  
Vol 19 (02) ◽  
pp. 371-395 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Image Processing ◽  
Digital Image Processing ◽  
Digital Image ◽  
Point Spread Function ◽  
Test Pattern ◽  
Upper Bounds ◽  
Noisy Signal ◽  
Information Theoretic ◽  
Point Spread ◽  
Spread Function

Motivated by applications in digital image processing, we discuss information-theoretic bounds to the amount of detail that can be recovered from a defocused, noisy signal. Mathematical models are constructed for test-pattern, defocusing and noise. Using these models, upper bounds are derived for the amount of detail that can be recovered from the degraded signal, using any method of image restoration. The bounds are used to assess the performance of the class of linear restorative procedures. Certain members of the class are shown to be optimal, in the sense that they attain the bounds, while others are shown to be sub-optimal. The effect of smoothness of point-spread function on the amount of resolvable detail is discussed concisely.

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