Linear versus logarithmic spatial filtering in the removal of multiplicative noises
1Department of Electrical Engineering, The University of Alabama, PO Box 6169, University, Alabama 35486, USA.
Optics Letters
|August 25, 2009
Summary
Linear and logarithmic spatial filtering effectively remove high-frequency image noise. Logarithmic filtering uniquely removes lower spatial frequency noise, outperforming linear methods in coherent-optical image processing.
Area of Science:
- Optics
- Image Processing
- Signal Processing
Background:
- Multiplicative noise degrades image quality in coherent-optical systems.
- Spatial filtering is a key technique for noise reduction.
Purpose of the Study:
- Compare linear and logarithmic coherent spatial-filtering techniques.
- Evaluate their effectiveness in separating multiplicative noise from images.
Main Methods:
- Utilized a coherent-optical image-processing system.
- Applied linear and logarithmic spatial-filtering methods.
- Assessed noise removal across various spatial frequencies.
Main Results:
- Both linear and logarithmic filtering effectively removed high-frequency grating-type noise.
- Linear filtering failed to remove noise below 5 lines/cm.
- Logarithmic filtering successfully removed noise at spatial frequencies lower than 5 lines/cm.
Conclusions:
- Logarithmic spatial filtering offers superior performance for multiplicative noise removal in coherent-optical systems.
- Logarithmic filtering is more versatile, handling a broader range of noise frequencies.
- The choice of filtering technique depends on the specific noise characteristics and required performance.
Related Concept Videos
01:28Applications of Logarithms
Logarithmic functions are powerful tools for simplifying the mathematical representation of phenomena involving exponential changes. Their ability to convert multiplicative relationships into additive ones is especially valuable in various scientific and engineering contexts. One notable application of logarithms is measuring sound intensity, specifically through the decibel (dB) scale used in acoustics.Sound intensity levels vary over an extensive range, from the faintest audible whisper to...
01:30Laws of Logarithms I
Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions are...
01:28Logarithmic Differentiation
When a car’s weight and driving forces act on a tire, they impose an external load on the rubber material. This load is resisted internally by forces distributed throughout the tire structure, which are defined as stress. The resulting deformation of the rubber due to this stress is quantified as strain. The relationship between stress and strain governs how the tire deforms under load and is central to understanding its mechanical response during operation.Rubber exhibits a nonlinear...
01:26Bode Plots
Bode plots are graphical tools that use logarithmic scales for frequency on the x-axis and gain in decibels on the y-axis. This logarithmic method allows a wide range of frequencies to be compactly displayed, enabling the analysis of component effects on circuit behavior across a broad frequency spectrum.
A network function represents the ratio of a system's output to its input, with the magnitude and phase angle derived from the complex network function. The decibel logarithmic gain is...
A network function represents the ratio of a system's output to its input, with the magnitude and phase angle derived from the complex network function. The decibel logarithmic gain is...
01:22Upsampling
Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
01:26Linear Approximation in Frequency Domain
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.