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| {{Merge from|Blind_deconvolution|date=April 2013}}
| | From comprehending the wedding party specialist you should consult to identifying ovulation with 100% precision, means that inside the book. Another point to consider is that sex should be enjoyable and not simply a chore. Getting pregnant has a lot to do with survival of the egg released during ovulation. Bear in mind, even a 10% reduction in body mass may help reestablish regular menstrual cycles and ovulation. after getting an avalanche of complaints from viewers, who said she was a horrible and unprofessional host. <br><br>Are you looking for some information on how to get pregnant step by step. need to have prior to travelling to a certain country. One fantastic program called Pregnancy Miracle offers a report for potential moms-to-be. You can direct Sims to fall in love and start their very own family. You might reason that both of you are young and healthy, so conceiving a child won't be a problem. <br><br>The recommended dosage is 500mg of vitamin C supplements daily, but you can go as high as 1000mg, but do not exceed more than 1000mg per day. ' It detects the LH surge which happens in the middle of Menstrual cycle, about 1 -1. Â Choose the best vitamins, Fertil - Aid for Women: Female Fertility Supplement">herbs and supplements that work for you in order to achieve your goal. If you look at this "infertility" issue from a holistic point of view, as shown in Pregnancy Miracle by Lisa Olson, you'll find that it is nothing but a mere imbalance in your body and that you can still find ways to correct it and produce a child. Alcohol can reduce fertility by as much as 50% and decrease sperm counts. <br><br>• Protein such as lean meat and chicken, fish, eggs and pulses (beans and lentils). Day one of your menstrual cycle is the day you first see menstrual blood loss even if it is only a drop of blood. If you are to the point where you feel like you have tried everything, even procedures like IVF, and everything has failed, then it is time to start really taking care of your body. But this time can differ based on lots of factors: anxiety degree, illness, transforming your natural environment and the like. All in all, the secret behind getting pregnant faster is to know your body inside out and to bring it into a healthy state. <br><br>In fact the baby continues to gain fat at the rate of half an ounce each and every day. Most of the infertility treatments undertaken by doctors have a list of possible side effects. Method 1 – Determining how to ‘read’ Cervical Fluid as a sign of the Best Time To Get Pregnant. If you've put off pregnancy schedule because of work or relationship concerns or because you simply weren't ready or tried but not "lucky" so to say, and you delay it until late 30's or even at 40's There's no denying your odds of getting pregnant are now far lower than at 20's. My oldest daughter had some issues in high school with her joints and she was unable to do some of her cheer leading moves because of it, but for the most part she was and is functioning normally.<br><br>Here is more info on [http://www.quebec-1759.info/sitemap/ is it possible to get pregnant on the pill] stop by our own site. |
| In [[mathematics]], '''deconvolution''' is an [[Algorithm|algorithm-based]] process used to reverse the effects of [[convolution]] on recorded data.<ref>{{cite web | author = O'Haver T | title = Intro to Signal Processing - Deconvolution | url = http://www.wam.umd.edu/~toh/spectrum/Deconvolution.html | publisher = University of Maryland at College Park | accessdate = 2007-08-15}}</ref> The concept of deconvolution is widely used in the techniques of [[signal processing]] and [[image processing]]. Because these techniques are in turn widely used in many [[science|scientific]] and [[engineering]] disciplines, deconvolution finds many applications.
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| In general, the object of deconvolution is to find the solution of a convolution equation of the form:
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| : <math>f * g = h \, </math>
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| Usually, ''h'' is some recorded signal, and ''ƒ'' is some signal that we wish to recover, but has been convolved with some other signal ''g'' before we recorded it. The function ''g'' might represent the [[transfer function]] of an instrument or a driving force that was applied to a physical system. If we know ''g'', or at least know the form of ''g'', then we can perform deterministic deconvolution. However, if we do not know ''g'' in advance, then we need to estimate it. This is most often done using methods of [[statistics|statistical]] [[estimation theory|estimation]].
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| In physical measurements, the situation is usually closer to
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| : <math>(f * g) + \varepsilon = h \, </math>
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| In this case ''ε'' is [[noise (physics)|noise]] that has entered our recorded signal. If we assume that a noisy signal or image is noiseless when we try to make a statistical estimate of ''g'', our estimate will be incorrect. In turn, our estimate of ''ƒ'' will also be incorrect. The lower the [[signal-to-noise ratio]], the worse our estimate of the deconvolved signal will be. That is the reason why [[inverse filter]]ing the signal is usually not a good solution. However, if we have at least some knowledge of the type of noise in the data (for example, [[white noise]]), we may be able to improve the estimate of ''ƒ'' through techniques such as [[Wiener deconvolution]].
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| The foundations for deconvolution and [[time-series analysis]] were largely laid by [[Norbert Wiener]] of the [[Massachusetts Institute of Technology]] in his book ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'' (1949).<ref>{{cite book |author=Wiener N |title=Extrapolation, Interpolation, and Smoothing of Stationary Time Series |publisher=MIT Press |location=Cambridge, Mass |year=1964 |isbn=0-262-73005-7}}</ref> The book was based on work Wiener had done during [[World War II]] but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of [[weather forecasting]] and [[economics]].
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| ==Applications of deconvolution==
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| ===Seismology===
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| The concept of deconvolution had an early application in [[reflection seismology]]. In 1950, [[Enders Robinson]] was a graduate student at [[MIT]]. He worked with others at MIT, such as [[Norbert Wiener]], [[Norman Levinson]], and economist [[Paul Samuelson]], to develop the "convolutional model" of a reflection [[seismogram]]. This model assumes that the recorded seismogram ''s''(''t'') is the convolution of an Earth-reflectivity function ''e''(''t'') and a [[seismic]] [[wavelet]] ''w''(''t'') from a [[point source]], where ''t'' represents recording time. Thus, our convolution equation is
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| :<math>s(t) = (e * w)(t). \, </math>
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| The seismologist is interested in ''e'', which contains information about the Earth's structure. By the [[convolution theorem]], this equation may be [[Fourier transform]]ed to
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| : <math>S(\omega) = E(\omega)W(\omega) \, </math>
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| in the [[frequency domain]]. By assuming that the reflectivity is white, we can assume that the [[Spectral density|power spectrum]] of the reflectivity is constant, and that the power spectrum of the seismogram is the spectrum of the wavelet multiplied by that constant. Thus,
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| : <math>|S(\omega)| \approx k|W(\omega)|. \, </math>
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| If we assume that the wavelet is [[minimum phase]], we can recover it by calculating the minimum phase equivalent of the power spectrum we just found. The reflectivity may be recovered by designing and applying a [[Wiener filter]] that shapes the estimated wavelet to a [[Dirac delta function]] (i.e., a spike). The result may be seen as a series of scaled, shifted delta functions (although this is not mathematically rigorous):
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| : <math>e(t)=\sum_{i=1}^N r_i\delta(t-\tau_i)</math>,
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| where ''N'' is the number of reflection events, ''τ''<sub> ''i''</sub> ''τ''<sub> ''i''</sub> are the reflection times of each event, and ''r''<sub> ''i''</sub> are the [[reflection coefficient]]s.
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| In practice, since we are dealing with noisy, finite [[Bandwidth (computing)|bandwidth]], finite length, [[Sampling (signal processing)|discretely sampled]] datasets, the above procedure only yields an approximation of the filter required to deconvolve the data. However, by formulating the problem as the solution of a [[Toeplitz matrix]] and using [[Levinson recursion]], we can relatively quickly estimate a filter with the smallest [[mean squared error]] possible. We can also do deconvolution directly in the frequency domain and get similar results. The technique is closely related to [[linear prediction]].
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| ===Optics and other imaging===
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| In optics and imaging, the term "deconvolution" is specifically used to refer to the process of reversing the [[Aberration in optical systems#Distortion of the image|optical distortion]] that takes place in an optical [[microscope]], [[electron microscope]], [[telescope]], or other imaging instrument, thus creating clearer images. It is usually done in the digital domain by a [[software]] [[algorithm]], as part of a suite of [[microscope image processing]] techniques. Deconvolution is also practical to sharpen images that suffer from fast motion or jiggles during capturing. Early [[Hubble Space Telescope]] images were distorted by a [[Hubble_Space_Telescope#Flawed_mirror|flawed mirror]] and could be sharpened by deconvolution.
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| The usual method is to assume that the optical path through the instrument is optically perfect, convolved with a [[point spread function]] (PSF), that is, a [[mathematical function]] that describes the distortion in terms of the pathway a theoretical [[point source]] of light (or other waves) takes through the instrument.<ref name=Pawley_2006>{{cite book |author = Cheng PC |chapter =The Contrast Formation in Optical Microscopy | title=Handbook of Biological Confocal Microscopy (Pawley JB, ed.) | publisher=Springer |location=Berlin |year=2006 | pages = 189–90 | edition = 3rd ed. |isbn=0-387-25921-X}}</ref> Usually, such a point source contributes a small area of fuzziness to the final image. If this function can be determined, it is then a matter of computing its [[Inverse function|inverse]] or complementary function, and convolving the acquired image with that. The result is the original, undistorted image.
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| In practice, finding the true PSF is impossible, and usually an approximation of it is used, theoretically calculated<ref>{{cite journal |author=Nasse M. J., Woehl J. C. |title=Realistic modeling of the illumination point spread function in confocal scanning optical microscopy |journal=J. Opt. Soc. Am. A |volume=27 |issue=2 |pages=295–302 |year=2010 |doi=10.1364/JOSAA.27.000295 |pmid=20126241}}</ref> or based on some experimental estimation by using known probes. Real optics may also have different PSFs at different focal and spatial locations, and the PSF may be non-linear. The accuracy of the approximation of the PSF will dictate the final result. Different algorithms can be employed to give better results, at the price of being more computationally intensive. Since the original convolution discards data, some algorithms use additional data acquired at nearby focal points to make up some of the lost information. [[Regularization (mathematics)|Regularization]] in iterative algorithms (as in [[expectation-maximization algorithm]]s) can be applied to avoid unrealistic solutions.
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| When the PSF is unknown, it may be possible to deduce it by systematically trying different possible PSFs and assessing whether the image has improved. This procedure is called ''[[blind deconvolution]]''.<ref name=Pawley_2006 /> Blind deconvolution is a well-established image restoration technique in [[astronomy]], where the point nature of the objects photographed exposes the PSF thus making it more feasible. It is also used in [[fluorescence microscopy]] for image restoration, and in fluorescence [[spectral imaging]] for spectral separation of multiple unknown [[fluorophore]]s. The most common [[Iteration|iterative]] algorithm for the purpose is the [[Richardson–Lucy deconvolution]] algorithm; the [[Wiener deconvolution]] (and approximations) are the most common non-iterative algorithms.
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| === Radio astronomy ===
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| When performing image synthesis in radio [[interferometry]], a specific kind of [[radio astronomy]], one step consists of deconvolving the produced image with the "dirty beam", which is a different name for the [[point spread function]]. A commonly used method is the [[CLEAN (algorithm)|CLEAN algorithm]].
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| == Absorption spectra ==
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| Deconvolution has been applied extensively to absorption spectra.<ref>{{cite book| last=Blass| first=W.E.| title=Deconvolution of Absorption Spectra|year=1981|publisher=Academic Press|isbn=0121046508|coauthors=Halsey, G.W.}}</ref> The [[:de:Van-Cittert-Dekonvolution|Van Cittert algorithm ]] (in German) may be used.<ref>{{cite journal|last=Wu|first=Chengqi|coauthors=Aissaoui, Idriss; Jacquey, Serge|title=Algebraic analysis of the Van Cittert iterative method of deconvolution with a general relaxation factor|journal=J. Opt. Soc. Am. A|year=1994|volume=11|issue=11|pages=2804–2808|doi=10.1364/JOSAA.11.002804}}</ref>
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| ==See also==
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| *[[Bit plane]]
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| *[[Digital filter]]
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| *[[Filter (signal processing)]]
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| *[[Filter design]]
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| *[[Minimum phase]]
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| *[[Independent component analysis]]
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| *[[Wiener deconvolution]]
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| *[[Richardson–Lucy deconvolution]]
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| *[[Digital room correction]]
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| *[[Free deconvolution]]
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| *[[Point spread function]]
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| *[[IVIVC]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| ;Presentations
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| * [http://www.leica-microsystems.com/science-lab/deconvolution/ Deconvolution: Leica Science Lab]
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| * [http://pichotjm.free.fr/Photos/Traitement/Deconv/Deconv.php Use of a deconvolution process to cancel complex motion/shake in photography](in French) [http://pichotjm.free.fr/Photos/Traitement/Deconv/Deconv2.php next and results by JM Pichot] Many photos, and no math!(in French)
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| * [http://visl.technion.ac.il/demos/bss Flash presentation of blind deconvolution and source separation problem]
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| ;Tutorials and techniques
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| * [http://micro.magnet.fsu.edu/primer/digitalimaging/deconvolution/deconvolutionhome.html Deconvolution in optical microscopy]
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| * [http://www.cv.nrao.edu/~abridle/deconvol/deconvol.html Deconvolution Tutorial]
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| <!-- ;Software
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| Please do not add software links without discussing them on the talk page first. -->
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| ;Other
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| * [http://www.ieee.org/organizations/history_center/oral_histories/transcripts/robinson_e.html Enders Robinson Oral History at IEEE]
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| [[Category:Signal processing]]
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| [[Category:Image processing]]
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From comprehending the wedding party specialist you should consult to identifying ovulation with 100% precision, means that inside the book. Another point to consider is that sex should be enjoyable and not simply a chore. Getting pregnant has a lot to do with survival of the egg released during ovulation. Bear in mind, even a 10% reduction in body mass may help reestablish regular menstrual cycles and ovulation. after getting an avalanche of complaints from viewers, who said she was a horrible and unprofessional host.
Are you looking for some information on how to get pregnant step by step. need to have prior to travelling to a certain country. One fantastic program called Pregnancy Miracle offers a report for potential moms-to-be. You can direct Sims to fall in love and start their very own family. You might reason that both of you are young and healthy, so conceiving a child won't be a problem.
The recommended dosage is 500mg of vitamin C supplements daily, but you can go as high as 1000mg, but do not exceed more than 1000mg per day. ' It detects the LH surge which happens in the middle of Menstrual cycle, about 1 -1. Â Choose the best vitamins, Fertil - Aid for Women: Female Fertility Supplement">herbs and supplements that work for you in order to achieve your goal. If you look at this "infertility" issue from a holistic point of view, as shown in Pregnancy Miracle by Lisa Olson, you'll find that it is nothing but a mere imbalance in your body and that you can still find ways to correct it and produce a child. Alcohol can reduce fertility by as much as 50% and decrease sperm counts.
• Protein such as lean meat and chicken, fish, eggs and pulses (beans and lentils). Day one of your menstrual cycle is the day you first see menstrual blood loss even if it is only a drop of blood. If you are to the point where you feel like you have tried everything, even procedures like IVF, and everything has failed, then it is time to start really taking care of your body. But this time can differ based on lots of factors: anxiety degree, illness, transforming your natural environment and the like. All in all, the secret behind getting pregnant faster is to know your body inside out and to bring it into a healthy state.
In fact the baby continues to gain fat at the rate of half an ounce each and every day. Most of the infertility treatments undertaken by doctors have a list of possible side effects. Method 1 – Determining how to ‘read’ Cervical Fluid as a sign of the Best Time To Get Pregnant. If you've put off pregnancy schedule because of work or relationship concerns or because you simply weren't ready or tried but not "lucky" so to say, and you delay it until late 30's or even at 40's There's no denying your odds of getting pregnant are now far lower than at 20's. My oldest daughter had some issues in high school with her joints and she was unable to do some of her cheer leading moves because of it, but for the most part she was and is functioning normally.
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