Generalized normal distribution - Revision history

en>Rajamanish: /* Maximum likelihood estimator */

2014-10-27T08:52:29Z

Maximum likelihood estimator

← Older revision		Revision as of 10:52, 27 October 2014
Line 1:		Line 1:
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en>Yobot: WP:CHECKWIKI error fixes + other fixes using AWB (9918)

2014-02-06T11:27:08Z

WP:CHECKWIKI error fixes + other fixes using AWB (9918)

← Older revision		Revision as of 13:27, 6 February 2014
Line 1:		Line 1:

	~~{{notability\|date=March 2009}}~~

	~~[[File:LiftingScheme.png\|thumb\|400px\|alt=Lifting Scheme.\|The (forward) Lifting Scheme transform block diagram.]]~~		It depends on the quality of the Wordpress theme but even if it's not a professional one you will be able to average 50-60$ EACH link. It is used by around 25% of all new websites, and there are more than 27 thousand plugins currently available. The effect is to promote older posts by moving them back onto the front page and into the rss feed. If you're using Wordpress and want to make your blog a "dofollow" blog, meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. Understanding how Word - Press works can be a challenge, but it is not too difficult when you learn more about it. <br><br>As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. The higher your blog ranks on search engines, the more likely people will find your online marketing site. We also help to integrate various plug-ins to expand the functionalities of the web application. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. W3C compliant HTML and a good open source powered by Word - Press CMS site is regarded as the prime minister. <br><br>The least difficult and very best way to do this is by acquiring a Word - Press site. By using Word - Press MLM websites or blogs, you and your companies presence on the internet can be created swiftly and simply. If Gandhi was empowered with a blogging system, every event in his life would have been minutely documented so that it could be recounted to the future generations. Provide the best and updated information to the web searchers and make use of these wonderful free themes and create beautiful websites. Customization of web layout is easy due to the availability of huge selection of templates. <br><br>It has become a more prevalent cause of infertility and the fertility clinic are having more and more couples with infertility problems. But the Joomla was created as the CMS over years of hard work. To do this, you should link your posts to other relevant posts that you've created. So, we have to add our social media sharing buttons in website. The popularity of Word - Press has increased the demand for Word - Press themes and these themes sells like hot cake on the internet. <br><br>Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. If you have any questions relating to in which and how to use [http://p-tweets.com/Ha0604 wordpress backup plugin], you can get hold of us at our web-site. Web developers and newbies alike will have the ability to extend your web site and fit other incredible functions with out having to spend more. Your topic is going to be the basis of your site's name.

	'~~''Generalized lifting scheme''' was developed by [http://gps~~-~~tsc.upc.es/imatge/_Joel/index~~.html Joel Solé] and [http://gps-tsc.upc.es/imatge/_Philippe/Philippe.html Philippe Salembier] and published in Joel's PhD Thesis.<ref>Ph.D. Thesis Dissertation: '''Optimization and Generalization of Lifting Schemes: Application to Lossless Image Compression'''</ref> It is ~~based on classical [[lifting scheme]]~~ and ~~generalizes it breaking out a restriction hidden in the scheme structure~~. ~~Classical lifting scheme has three kind of operations.~~
	~~# '''Lazy wavelet transform''' splits signal <math>f_j[n]</math> in two new signals:~~ the ~~odd samples signal denoted by <math>f_j^o[n]</math>~~ and the ~~even samples signal denoted by <math>f_j^e[n]</math>~~.
	# '~~''Prediction step''' its objective is compute~~ a ~~prediction for the odd samples~~, ~~based~~ on the ~~even samples (or vice versa). This prediction is subtracted from the odd samples creating an error signal <math>g_{j+1}[n]</math>.~~
	~~# '''Update step''' This step recalibrates the low frequency branch with some~~ of the ~~energy removed during subsampling~~. ~~In the case of classical Lifting~~, ~~this~~ is ~~used in order to "prepare" the signal for the next prediction step~~. ~~It uses the predicted odd samples~~ <~~math~~>~~g_{j+1}[n]~~<~~/math~~> to ~~prepare the even ones <math>f_j^e[n]</math> (or vice versa)~~. ~~This update is subtracted from~~ the ~~even samples producing the signal denoted by <math>f_{j+1}[n]</math>~~.

	~~The scheme is invertible due~~ to the ~~structure~~ of ~~itself. In~~ the ~~[[Receiver (information theory)\|receiver]] the update step is computed first~~. ~~Its result~~ is ~~added~~ to ~~the even samples. After that~~, ~~it's possible to compute exactly~~ the ~~same prediction~~ and ~~add it to~~ the ~~odd samples~~. ~~In order to recover~~ the ~~original signal, we have~~ to ~~invert the Lazy Wavelet Transform. Generalized lifting scheme has the same three kind of operations. However~~ this ~~scheme avoids the addition~~-~~subtraction restriction that offered Classical Lifting~~. ~~That fact has some consequences. For example~~, the ~~design of all steps must guarantee the scheme invertibility (not guaranteed if the addition-subtraction restriction is avoided)~~.

	~~== Definition ==~~
	~~[[File:GLScheme.png\|thumb\|400px\|alt=Generalized Lifting Scheme.\|The (forward) Generalized Lifting Scheme transform block diagram.]]~~

	~~''Generalized lifting scheme'' is~~ a ~~dyadic transform~~ that ~~follows~~ the ~~next rules:~~
	~~# Computes a '''Lazy Wavelet Transform'''~~ and ~~splits even samples from odd samples.~~
	~~# Computes a '''Prediction [[Map (mathematics)\|Mapping]]'''. This step tries~~ to ~~predict odd samples taking into account~~ the ~~even ones (or vice versa)~~. ~~This a mapping from the space~~ of ~~the samples in <math>f_j^e[n]</math>~~ to the ~~space~~ of ~~the samples in <math>g_{j+1}[n]</math>~~. ~~In this case the samples (from~~ <~~math~~>~~f_j^e[n]~~<~~/math~~>~~) chosen to be~~ the ~~reference for <math>f_j^o[n]</math>~~ are ~~called '''~~the ~~context'''~~. ~~It could be expressed as:~~
	~~#:<math> \textstyle g_{j+1}[n] = P(f_j^o[n];f_j^e[n]) </math>~~
	~~# Computes an '''Update Mapping''~~'. ~~This step tries~~ to ~~update the even samples taking into account the odd predicted samples~~. ~~It would be a kind~~ of ~~preparation~~ for the ~~next prediction step, if any~~. ~~It could be expressed:~~
	#:<~~math~~> ~~\textstyle f_{j+1}[n] = U(f_j^e[n];f_{j+1}[n])~~ <~~/math~~>

	~~Obviously, these mapping cannot~~ be ~~any function. In order~~ to ~~guarantee~~ the ~~invertibility of the scheme itself, all mapping involved~~ in the transform, must be invertible. In case that mappings arise and arrive on finite sets (discrete bounded value signals), this condition is equivalent to say that mappings are [[Injective function\|injective]] (one-to-one). Moreover, if mapping goes from one set to a ~~set~~ of ~~the same cardinality, it~~ should ~~be [[Bijection\|bijective]].~~

	In the ~~Generalized Lifting Scheme~~ the ~~addition/subtraction restriction is avoided~~ by ~~including this~~ step in the ~~mapping~~. ~~In this way~~ the ~~Classical Lifting Scheme is generalized.~~

	~~== Design ==~~
	~~Nowadays~~, ~~it has been developed some designs for the prediction step mapping. The update step design is not considered at the moment~~, ~~because there isn't any answers for~~ the ~~question: ''what does the update step is useful for?''. The main application~~ of ~~this technique is the image compression. There some interesting references such as~~,~~<ref>{{cite conference \| last1 = Rolon \| first1 = J~~. C. ~~\| last2 = Salembier \| first2 = P. \| title = Generalized Lifting for Sparse Image Representation and Coding \| booktitle = Picture Coding Symposiu~~, ~~PCS 2007 \| date = Nov 7~~-~~9, 2007}}</ref><ref>{{cite conference \| last1 = Rolon \| first1 = J. C. \| last2 = Salembier \| first2 = P~~. ~~\| last3 = Alameda \| first3 = X. \| title = Image Compression with Generalized Lifting~~ and ~~partial knowledge of~~ the ~~signal pdf \| booktitle = International Conference on Image Processing, ICIP'08 \| date = Oct 12-15, 2008}}</ref><ref>{{cite conference \| last1 = Rolon \| first1 = J~~. ~~C. \| last2 = Ortega \| first2 = A. \| last3 = Salembier \| first3 = P. \| title = Modeling~~ of Contours in Wavelet Domain for Generalized Lifting Image Compression \| booktitle = ICASSP 2009 (submitted)}}</ref> and.<ref>{{cite conference \| last1 = Rolon \| first1 = J. C. \| last2 = Mendonça \| first2 = E. \| last3 = Salembier \| first3 = P. ~~\| title = Generalized Lifting With Adaptive Local pdf estimation for Image Coding}}</ref>~~

	~~== References ==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Generalized Lifting}}~~
	~~[[Category:Wavelets]]~~

en>Nanite: moving versions into their respective sections

2014-01-30T16:54:20Z

moving versions into their respective sections

← Older revision		Revision as of 18:54, 30 January 2014
Line 1:		Line 1:
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			[[File:LiftingScheme.png\|thumb\|400px\|alt=Lifting Scheme.\|The (forward) Lifting Scheme transform block diagram.]]

			'''Generalized lifting scheme''' was developed by [http://gps-tsc.upc.es/imatge/_Joel/index.html Joel Solé] and [http://gps-tsc.upc.es/imatge/_Philippe/Philippe.html Philippe Salembier] and published in Joel's PhD Thesis.<ref>Ph.D. Thesis Dissertation: '''Optimization and Generalization of Lifting Schemes: Application to Lossless Image Compression'''</ref> It is based on classical [[lifting scheme]] and generalizes it breaking out a restriction hidden in the scheme structure. Classical lifting scheme has three kind of operations.
			# '''Lazy wavelet transform''' splits signal <math>f_j[n]</math> in two new signals: the odd samples signal denoted by <math>f_j^o[n]</math> and the even samples signal denoted by <math>f_j^e[n]</math>.
			# '''Prediction step''' its objective is compute a prediction for the odd samples, based on the even samples (or vice versa). This prediction is subtracted from the odd samples creating an error signal <math>g_{j+1}[n]</math>.
			# '''Update step''' This step recalibrates the low frequency branch with some of the energy removed during subsampling. In the case of classical Lifting, this is used in order to "prepare" the signal for the next prediction step. It uses the predicted odd samples <math>g_{j+1}[n]</math> to prepare the even ones <math>f_j^e[n]</math> (or vice versa). This update is subtracted from the even samples producing the signal denoted by <math>f_{j+1}[n]</math>.

			The scheme is invertible due to the structure of itself. In the [[Receiver (information theory)\|receiver]] the update step is computed first. Its result is added to the even samples. After that, it's possible to compute exactly the same prediction and add it to the odd samples. In order to recover the original signal, we have to invert the Lazy Wavelet Transform. Generalized lifting scheme has the same three kind of operations. However this scheme avoids the addition-subtraction restriction that offered Classical Lifting. That fact has some consequences. For example, the design of all steps must guarantee the scheme invertibility (not guaranteed if the addition-subtraction restriction is avoided).

			== Definition ==
			[[File:GLScheme.png\|thumb\|400px\|alt=Generalized Lifting Scheme.\|The (forward) Generalized Lifting Scheme transform block diagram.]]

			''Generalized lifting scheme'' is a dyadic transform that follows the next rules:
			# Computes a '''Lazy Wavelet Transform''' and splits even samples from odd samples.
			# Computes a '''Prediction [[Map (mathematics)\|Mapping]]'''. This step tries to predict odd samples taking into account the even ones (or vice versa). This a mapping from the space of the samples in <math>f_j^e[n]</math> to the space of the samples in <math>g_{j+1}[n]</math>. In this case the samples (from <math>f_j^e[n]</math>) chosen to be the reference for <math>f_j^o[n]</math> are called '''the context'''. It could be expressed as:
			#:<math> \textstyle g_{j+1}[n] = P(f_j^o[n];f_j^e[n]) </math>
			# Computes an '''Update Mapping'''. This step tries to update the even samples taking into account the odd predicted samples. It would be a kind of preparation for the next prediction step, if any. It could be expressed:
			#:<math> \textstyle f_{j+1}[n] = U(f_j^e[n];f_{j+1}[n]) </math>

			Obviously, these mapping cannot be any function. In order to guarantee the invertibility of the scheme itself, all mapping involved in the transform, must be invertible. In case that mappings arise and arrive on finite sets (discrete bounded value signals), this condition is equivalent to say that mappings are [[Injective function\|injective]] (one-to-one). Moreover, if mapping goes from one set to a set of the same cardinality, it should be [[Bijection\|bijective]].

			In the Generalized Lifting Scheme the addition/subtraction restriction is avoided by including this step in the mapping. In this way the Classical Lifting Scheme is generalized.

			== Design ==
			Nowadays, it has been developed some designs for the prediction step mapping. The update step design is not considered at the moment, because there isn't any answers for the question: ''what does the update step is useful for?''. The main application of this technique is the image compression. There some interesting references such as,<ref>{{cite conference \| last1 = Rolon \| first1 = J. C. \| last2 = Salembier \| first2 = P. \| title = Generalized Lifting for Sparse Image Representation and Coding \| booktitle = Picture Coding Symposiu, PCS 2007 \| date = Nov 7-9, 2007}}</ref><ref>{{cite conference \| last1 = Rolon \| first1 = J. C. \| last2 = Salembier \| first2 = P. \| last3 = Alameda \| first3 = X. \| title = Image Compression with Generalized Lifting and partial knowledge of the signal pdf \| booktitle = International Conference on Image Processing, ICIP'08 \| date = Oct 12-15, 2008}}</ref><ref>{{cite conference \| last1 = Rolon \| first1 = J. C. \| last2 = Ortega \| first2 = A. \| last3 = Salembier \| first3 = P. \| title = Modeling of Contours in Wavelet Domain for Generalized Lifting Image Compression \| booktitle = ICASSP 2009 (submitted)}}</ref> and.<ref>{{cite conference \| last1 = Rolon \| first1 = J. C. \| last2 = Mendonça \| first2 = E. \| last3 = Salembier \| first3 = P. \| title = Generalized Lifting With Adaptive Local pdf estimation for Image Coding}}</ref>

			== References ==
			{{Reflist}}

			{{DEFAULTSORT:Generalized Lifting}}
			[[Category:Wavelets]]

en>Kilom691: ref changed for coherence

2012-07-27T16:59:36Z

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