Add Denoising Problem

[MohamedLaghdafHABIBOULLAH]

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[codecov]

Codecov Report

Attention: Patch coverage is 71.55963% with 31 lines in your changes are missing coverage. Please review.

Project coverage is 92.75%. Comparing base (9926db3) to head (43a4833).

❗ Current head 43a4833 differs from pull request most recent head abe7265. Consider uploading reports for the commit abe7265 to get more accurate results

Files	Patch %	Lines
src/denoising_data.jl	63.52%	31 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #43      +/-   ##
==========================================
- Coverage   99.16%   92.75%   -6.42%     
==========================================
  Files          10       12       +2     
  Lines         360      469     +109     
==========================================
+ Hits          357      435      +78     
- Misses          3       34      +31     

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[dpo]

Thank you for all this. Do obj and grad! allocate? could you show some benchmarks?

[MohamedLaghdafHABIBOULLAH]

Thank you for all this. Do obj and grad! allocate? could you show some benchmarks?

Sure there it is :

julia> model, sol = denoising_model((n, m), (n_p, m_p), kz, kt);

julia> x,y = ones(n * m), rand(n * m);

julia> @benchmark obj($model, $x)
BenchmarkTools.Trial: 2017 samples with 1 evaluation.
 Range (min … max):  1.893 ms … 23.679 ms  ┊ GC (min … max): 0.00% … 65.07%
 Time  (median):     2.307 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   2.479 ms ±  1.012 ms  ┊ GC (mean ± σ):  6.94% ± 12.51%

   ▂ ▃█▂                                                      
  ▆█▇███▅▆▇▄▄▁▃▄▄▁▃▃▃▁▁▁▁▁▃▁▁▁▁▃▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃▅█▇ █
  1.89 ms      Histogram: log(frequency) by time     7.45 ms <

 Memory estimate: 8.21 MiB, allocs estimate: 585.

julia> @benchmark grad!($model, $y, $x)
BenchmarkTools.Trial: 1061 samples with 1 evaluation.
 Range (min … max):  3.418 ms … 19.016 ms  ┊ GC (min … max):  0.00% … 78.02%
 Time  (median):     4.221 ms              ┊ GC (median):     0.00%
 Time  (mean ± σ):   4.713 ms ±  1.945 ms  ┊ GC (mean ± σ):  10.12% ± 15.49%

   ▁▅██▅▃▁                                                    
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  3.42 ms      Histogram: log(frequency) by time     14.9 ms <

 Memory estimate: 17.42 MiB, allocs estimate: 1165.

[geoffroyleconte]

Thanks for this PR! I also added a few comments to try to reduce some allocations.

[geoffroyleconte]

It might be possible to reduce the allocations even more the allocation by preallocating and using in-place fft etc..., but I'm not sure that they exist. Maybe we can merge and open an issue saying that we can improve the allocations if needed.

[MohamedLaghdafHABIBOULLAH]

@dpo normalement j'ai tenu compte de tous tes commentaires dans cette PR

[dpo]

Does this model only work in Float64? Could sigma be made generic?

[MohamedLaghdafHABIBOULLAH]

In the literature, no one seemed to be interested by this problem at lower precision.
I'm also afraid, that the wavelet or Fourier transform might not be generic. I should check.

[dpo]

Are there in-place versions of H and W_T? Currently, there are lots of allocations here.

[dpo]

@MohamedLaghdafHABIBOULLAH Could you please rebase this PR?