Application of Chebechev's inequality theorem in the design of optimal non-linear filters

2002 ◽  
Author(s):  
S. Challa ◽  
F.A. Faruqi
Keyword(s):  
Linear Filters ◽  
Non Linear ◽  
Inequality Theorem

scholarly journals SPATIO-TEMPORAL DATA ANALYSIS WITH NON-LINEAR FILTERS: BRAIN MAPPING WITH fMRI DATA

2011 ◽  
Vol 19 (3) ◽  
pp. 189
Author(s):  
Karsten Rodenacker ◽  
Klaus Hahn ◽  
Gerhard Winkler ◽  
Dorothea P Auer
Keyword(s):  
Signal To Noise Ratio ◽  
Three Dimensional ◽  
Digital Data ◽  
Linear Filters ◽  
Brain Functions ◽  
Non Linear ◽  
Long Time ◽  
Spatio Temporal ◽  
Sensory Activation ◽  
Temporal Data Analysis

Spatio-temporal digital data from fMRI (functional Magnetic Resonance Imaging) are used to analyse and to model brain activation. To map brain functions, a well-defined sensory activation is offered to a test person and the hemodynamic response to neuronal activity is studied. This so-called BOLD effect in fMRI is typically small and characterised by a very low signal to noise ratio. Hence the activation is repeated and the three dimensional signal (multi-slice 2D) is gathered during relatively long time ranges (3-5 min). From the noisy and distorted spatio-temporal signal the expected response has to be filtered out. Presented methods of spatio-temporal signal processing base on non-linear concepts of data reconstruction and filters of mathematical morphology (e.g. alternating sequential morphological filters). Filters applied are compared by classifications of activations.

scholarly journals A new family of non-linear filters for background subtraction of wide-field surveys

1996 ◽  
Vol 317 (2) ◽  
pp. 95-100 ◽  
Author(s):  
V. S. Shergin ◽  
A. Yu. Kniazev ◽  
V. A. Lipovetsky
Keyword(s):  
Background Subtraction ◽  
Wide Field ◽  
Linear Filters ◽  
Field Surveys ◽  
New Family ◽  
Non Linear

A general recursive discrete-time filter

1993 ◽  
Vol 30 (3) ◽  
pp. 575-588 ◽  
Author(s):  
Robert J. Elliott
Keyword(s):  
Discrete Time ◽  
Conditional Density ◽  
Linear Filters ◽  
Non Linear ◽  
Information Patterns

A reference probability is explicitly constructed under which the signal and observation processes are independent. A simple, explicit recursive form is then obtained for the conditional density of the signal given the observations. Both non-linear and linear filters are considered, as well as two different information patterns.

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