Editing User:Ozzy
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== O: Only out of interest == | == O: Only out of interest == | ||
* Did you ever hear about Octave before? | * Did you ever hear about Octave before? | ||
''Yes I did. | ''Yes I did.'' | ||
** If so, when and where? How far have you been involved already? | ** If so, when and where? How far have you been involved already? | ||
''I am using Octave in daily basis for my research work and I actually prefer it over Matlab due to relaxed syntax, easy access to additional packages and lower price ;)'' | ''I am using Octave in daily basis for my research work and I actually prefer it over Matlab due to relaxed syntax, easy access to additional packages and lower price ;)'' | ||
* What was the first question concerning Octave you could not find an answer to rather quickly? | * What was the first question concerning Octave you could not find an answer to rather quickly? | ||
''Unfortunately there was a lot of them and they mostly | ''Unfortunately there was a lot of them and they mostly include poorly documented packages'' | ||
== P: Prerequisites == | == P: Prerequisites == | ||
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== S: Self-assessment == | == S: Self-assessment == | ||
* Please describe how useful criticism looks from your point of view as committing student. | * Please describe how useful criticism looks from your point of view as committing student. | ||
* How autonomous are you when developing? | * How autonomous are you when developing? ''If you answer both subquestions with "Yes, definitely", we are a tad confused. ;-)'' | ||
** Do you like to discuss changes intensively and not start coding until you know what you want to do? | ** Do you like to discuss changes intensively and not start coding until you know what you want to do? | ||
** Do you like to code a proof of concept to 'see how it turns out', modifying that and taking the risk of having work thrown away if it doesn't match what the project or original proponent had in mind? | ** Do you like to code a proof of concept to 'see how it turns out', modifying that and taking the risk of having work thrown away if it doesn't match what the project or original proponent had in mind? | ||
== Y: Your task == | == Y: Your task == | ||
* Did you select a task from our list of proposals and ideas? | * Did you select a task from our list of proposals and ideas? | ||
** If yes, what task did you choose? Please describe what part of it you especially want to focus on if you can already provide this information. ''Please also wiki-link the page for your elaborated proposal here.'' | ** If yes, what task did you choose? Please describe what part of it you especially want to focus on if you can already provide this information. ''Please also wiki-link the page for your elaborated proposal here.'' | ||
** If you apply for a task you have added yourself instead, please describe this task, its scope and people you already talked to concerning it. What field of tasks did you miss on the list? | ** If you apply for a task you have added yourself instead, please describe this task, its scope and people you already talked to concerning it. What field of tasks did you miss on the list? | ||
I would like to implement a general algorithm for maximum entropy reconstruction. This is an algorithm for estimating distributions and have applications in various inverse or ill-posed problems. It is used for deblurring/deconvolution of images, power spectrum estimation, smoothing, measurement data processing in biology, physics and more. | |||
The algorithm would find its place in one of the existing packages (where ''optim'' or ''signal'' sound appropriate) or as a separate package. I plan to prepare two versions of the general algorithm, (temporal name {{codeline|maxent}}) | |||
* a version for problems defined by matrix. The function's declaration should be something like this | |||
{{Code|Linear problem declaration|<syntaxhighlight lang="octave" style="font-size:13px">function [x,info,...]=maxent(y,D,sigma,alpha=0.95, model=1, optset) | |||
</syntaxhighlight>}} | |||
where {{codeline|y} is the data vector, and {{codeline|D}} is the transformation matrix. {{codeline|sigma}} should be a vector or scalar which describes standard deviation of values of {{codeline|y}}. The optional parameter {{codeline|alpha}} and {{codeline|model}} describe confidence and a priori distribution of {{codeline|x}} (defaults to flat) respectively. The last parameter {{codeline|optset}} would allow to pass additional parameters to function, similar to the ones in {{codeline|optim}} package. | |||
The returned value {{codeline|x}} is such that | |||
<math> y \approx Dx</math> | |||
where each of the coordinates of {{codeline|y}} lies within {{codeline|alpha}} confidence interval (normal distributed error assumed). Out of all possible {{codeline|x}} the one with the highest entropy is chosen. {{codeline|info}} describes the convergence of the algorthm. The other returned parameters will describe final gradients, Hessians and Lagrange's coefficient. | |||
* another version would be defined for a non-linear function. The declaration would very similar | |||
{{Code|Linear problem declaration|<syntaxhighlight lang="octave" style="font-size:13px">function [x,info,...]=maxent(y,fun,sigma,alpha=0.95, model=1, optset) | |||
</syntaxhighlight>}} | |||
All the parameters have the similar meaning here, and the new parameter {{codeline|fun}} is the handle to a function which accepts vector argument, which describes the problem to be inverted. This time the returned value should obey | |||
<math> y \approx f(x)</math> | |||
It is convienient to have this version of the algorithm for problem where obtaining the transformation matrix is difficult to compute or affects performance (think fft). The algorithm is expected to give good results for linear functions. For not-too-complicated non-linear cases the chances are still there. | |||
Additional work will be put to provide some wrapper functions to allow the user quickly use MEM in their problem. This includes function for 1D and image deconvolutions, time series components analysis, power spectral estimation and other applications I will be able to find in Matlab or other computational software. | |||
* Please provide a rough estimated timeline for your work on the task. ''This should include the GSoC midterms and personal commitments like exams or vacation ("non-coding time"). Optionally include two or three milestones you expect.'' | |||
[[Category: Summer of Code]] | [[Category: Summer of Code]] |