Thanks for this package! I'm trying to learn about the implementation details of idwt, but totally flummoxed as to where to look. I believe the key functions are defined with metaprogramming at:

And they are all effectively wrappers around:

where for dwt, fw=true and for iwt, fw=false. This leads to a key branch in the code,

I am running this package on Julia Version 0.4.1-pre+8.
When using Wavelets, four kinds of deprecation warning appear:

• Base.String is deprecated, use AbstractString instead..
• Base.FloatingPoint is deprecated, use AbstractFloat instead.
• Base.Nothing is deprecated, use Void instead.
• Union(args...) is deprecated, use Union{args...} instead.

The warnings will become errors when v0.5 lands.
What is the compatibility policy for this package ?

The current implementations of the mutating versions of the transforms require that the input array x and output array y have the same eltype:

function _dwt!(y::AbstractVector{T}, x::AbstractVector{T},
                filter::OrthoFilter, L::Integer, fw::Bool) where T<:Number

It would be useful to relax this restriction, e.g.:

function _dwt!(y::AbstractVector{Ty}, x::AbstractVector{Tx},
                filter::OrthoFilter, L::Integer, fw::Bool) where {Tx<:Number, Ty<:Number}

Note that the most basic "do nothing" transform in the code reverts to simply copyto!(y,x), and copyto! itself does not require the arguments do have the same eltype. (Of course you get and InexactError if you try to copy from arbitrary Floats to Ints, or Real to Complex, but if you do precision changes like Float32 to Float64 then copyto! takes care of the conversion for you.
I'd be willing to try to make PR to provide this generality, because I think it just requires some changes to the function declarations, but I wanted to see first if there are objections or drawbacks.
Edit: I needed this for my work so I made the PR #54.

For construction of wavelet transform types, the currect API is

wavelet("db2"; transform="filter", boundary="per")

Any thoughts whether using symbols

wavelet("db2"; transform=:filter, boundary=:per)

or types

wavelet("db2"; transform=FilterWavelet(), boundary=PerBoundary())
# or using const objects
wavelet("db2"; transform=FilterWT, boundary=PerWB)

might be better, or more elegant?

I may have missed it but some references for the algorithms and wavelets implemented in the README or in other docs would be hugely helpful.

Hope this is appropriate to raise here.

Running the example code transform1d.jl results in the error message
MethodError: no method matching wavelet(::Wavelets.WT.CDF{9, 7}, ::Wavelets.WT.FilterTransform)
occurring for the line

wavelet(WT.cdf97, WT.Filter)

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Hi,

Would it be hard to implement the 3d transforms? I am interested in doing 3d transforms.

Thanks

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Apologies if I am missing something very basic (I am only just learning about wavelets), but I believe there is a bug in dwt:

n = 2^6 - 1
u = cos.(2*pi*range(0, stop=1, length=n))
wav = wavelet(WT.haar) # also tested WT.db2
w = dwt(u, wav)
display(w == u)

This code returns true. Expected behaviour is that w is the discrete wavelet transform of u, something like I get running the same experiment in Mathematica.

Version info:

Wavelets 0.9.4
Julia 1.6.3

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Is there any way to create an undecimated DWT as of now?

If not, are there any plans?

I a hope I am not missing anything but I could not find the layout of the coefficient vector. Inspecting the size of the coefficient also does not immediately suggest a certain order to me.

Since the CDF 9/7 basis is not orthogonal, the inverse transform matrix is not the adjoint (or transpose) of the forward transform matrix. Would it be possible to modify the idwt() function, such that the use of idwt() with an adjoint=true flag simply returns the action of the transpose of idwt with the cdf 9/7 basis on a given vector? This would be very useful for change of basis problems where the adjoint of the inverse transform from cdf 9/7 to cartesian is required in applying the chain rule.

julia> y = dwt(x, wavelet(WT.cdf97, WT.Filter))
ERROR: MethodError: wavelet has no method matching wavelet(::Wavelets.WT.CDF{9,7}, ::Wavelets.WT.FilterTransform)
Closest candidates are:

Ref https://discourse.julialang.org/t/package-compatibility-caps/15301

and

https://github.com/JuliaRegistries/General/tree/master/W/Wavelets

Hi, may I know if you are planning to write 2D WPT as shown in the To-do list? If so, when will it be available? Thanks.

I have tried this package (much appreciated!) with an application to compressed sensing and it seems that currently the dwt and its inverse cannot be applied to complex numbers. Would be great if this could be solved by relaxing the type definitions.

Hi,

please tag a release. current master branch has updated Project.toml.

I'm trying to implement a soft thresholding method for 3D data which preserves scaling (or approximation) coefficients at each level, then soft thresholds all others. Unfortunately, I have been having trouble identifying indices which correspond to the scaling coefficients. I was trying to make sense of the detailn() and detailindex() functions and it makes sense to me for 1D condition, but I don't understand how to use these to create an index list for higher dimensions, like the 3D condition that I need.

Also to complicate further, I need to handle both dyadic cube and dyadic non-cube dimensions.

Could someone help me with this?

Thanks

Hi,

Would you be interested in a procedure for computing Daubechies filter coefficients? (Instead of looking them up in a dict)

Best,

Robert

Hi! I recently was reading about wavelets, and I noticed that just recently there was a paper (and corrisponding code) on an implementation of the continous wavelet transform that had performance gains of ~30-120 times faster. Not sure if this is within the scope of this package, but I figured it might be something that would be applicable :)

Morlet wavelet analysis is needed in the analysis of waves. I hope it can be implemented.

Hi, I get various deprecation messanges under Julia 0.6. It seems they are resolved on Master. Could you make release @gummif?

Thanks,

Tobi

Dear All,

I am working on Ph.D research and I would like to implement lifting transform of image using haar or any other using julia but i am not getting code for the same please help me and provide code.

Thanks

Manoj Pandey
PhD scholar
GGU
India

Implementing #42, I noticed filter definitions are different in this package than in at least one other wavelet package I've used (wmtsa in R). The code below plots the equivalently-named wavelets from these two packages.

using Wavelets
using Plots
using RCall; R"library(wmtsa)"

julia_wavelets = [:coif6, :db2, :db4, :db6, :db8, :db10, :haar, :sym4, :sym6, :sym8]
r_wavelets = ["c6", "d2", "d4", "d6", "d8", "d10", "haar", "s4", "s6", "s8"]

subplots = []
for (wj, wr) in zip(julia_wavelets, r_wavelets)
    hr = Array(reval("wavDaubechies('$wr')")[:wavelet])
    gr = Array(reval("wavDaubechies('$wr')")[:scaling])
    p = plot(hr, color=:pink, label="Wavelet (R)", 
        title="Julia: $(String(wj)), R: $wr", 
        background_color_legend=:transparent, size=(600, 1000))
    plot!(p, gr, color=:red, label="Scaling (R)")

    g, h = @eval WT.makeqmfpair(wavelet(WT.$wj))
    plot!(p, h, color=:lightblue, label="Wavelet (Julia)")
    plot!(p, g, color=:blue, label="Scaling (Julia)")
    push!(subplots, p)
end
plot(subplots..., layout=(5,2))

This may just be a Pepsi/Coke problem with slightly different definitions, but it seemed worth double-checking.

Hi,

I've been working on a patch which relaxes the requirement that the signals have dyadic support, in favour of a "sufficient powers of 2" test. To compute an n-level transform, the support of the signal needs only to have 2^n as a factor. I've completed the modifications and tested them on an older version of the package, before the significant changes which have been made of the last couple of months.

The reason for this issue is this: If I integrate these changes into the current version of the package, are you likely to accept them? (Assuming you're happy with the technical quality?)

And a further question: Do you plan any further significant changes to the API soon? Ought I to wait for some upcoming change before rebasing my work?

Thanks

Andy

The SpecialFunctions package is now a few versions farther along; in particular it jumped from 0.10 to 1.x.
I have tested and current Wavelets is compatible with 1.2 so it would be very helpful for packages that rely on Wavelets to have Project.toml show compatibility with 1.x. Thanks.

Wavelet filters are typically scaled to have unit energy and sum to sqrt(2.0); this simplifies a number of equations and transforms. So why are these wavelet families different?

Battle-Lemarie filters

sumabs2(FILTERS["batt2"]) = 0.5; sum(FILTERS["batt2"]) = 1.0
sumabs2(FILTERS["batt4"]) = 0.5; sum(FILTERS["batt4"]) = 1.0
sumabs2(FILTERS["batt6"]) = 0.5; sum(FILTERS["batt6"]) = 1.0

symlets

sumabs2(FILTERS["sym4"]) = 2.0; sum(FILTERS["sym4"]) = 2.0
sumabs2(FILTERS["sym5"]) = 2.0; sum(FILTERS["sym5"]) = 2.0
sumabs2(FILTERS["sym6"]) = 2.0; sum(FILTERS["sym6"]) = 2.0
sumabs2(FILTERS["sym7"]) = 2.0; sum(FILTERS["sym7"]) = 2.0
sumabs2(FILTERS["sym8"]) = 2.0; sum(FILTERS["sym8"]) = 2.0
sumabs2(FILTERS["sym9"]) = 2.0; sum(FILTERS["sym9"]) = 2.0
sumabs2(FILTERS["sym10"]) = 2.0; sum(FILTERS["sym10"]) = 2.0

I realize that Matlab's wavelet toolbox scales symlets to have energy ~0.5, so this isn't the only wavelet toolbox that uses unusual scaling for symlets; but why this particular choice?

Hi, my team has developed an extension to your package Wavelets.jl which contains 2D-WPT, stationary transforms, group operations on signals (best basis, denoising, feature extraction). It would be really helpful if you could add a link to our package in your README.md, so that users are aware of these functions and operations in Julia.

The function is still under continuous development, but most of the functions that I've mentioned above are stable. Feel free to check out WaveletsExt.jl and its documentations and let me know if you'd be happy to add WaveletsExt.jl to your link, or if more improvements and developments are needed before you do so. Thanks!

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Could this package have a build in api for calculating wavelet coherency? it's a very import method for neuroscience :D

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I am working with non-squared matrix 2D (x != y) or 3D (x != y != z).
For example an image of 220 x 160, when applying the DWT it apply a DWT of level 2 (restricted by the size 220)

1. Is that possible to perform a multilevel fully separable decomposition WT like :
   https://pywavelets.readthedocs.io/en/latest/ref/nd-dwt-and-idwt.html#multilevel-fully-separable-decomposition-fswavedecn
   I did not find the function for that but maybe I am missing something :)

2. An other approach will be to pad the data. In that case does the operator is still orthogonal (Adjoint = Inverse)

Thanks :)

Is it possible to add quincunx bases to obtain nonseparable transforms? Separable 2D transforms have directional-amplification artifacting. (I have not been able to get a handle on the rotation maths for this, so I don't know if this is even possible with the J code.) For example...
https://www.mathworks.com/matlabcentral/fileexchange/13507-lisq-a-toolbox-for-the-lifting-scheme-on-2d-quincunx-grids

I am sure I am missing something but I when I run dwt I can only see the first level wavelet detail coefficients. How can I see the other levels?

Hi,

Say I create a filter:

julia> using Wavelets

julia> F = waveletfilter("db2")
Wavelets.WaveletTypes.OrthoFilter{Wavelets.WaveletTypes.PerBoundary}([0.4829629131445342,0.8365163037378079,0.22414386804201344,-0.12940952255126031],"db2")

How do I extract the vector of numbers from F?

I've been looking in the code, but I can't seem to figure this out.

Thanks,

Robert

wplotim modifies the argument x it receives. I think either the function should be renamed to wplotim!
or on line 83 of Plot.jl xts = x should be changed to xts = copy(x) (which seems the best option to me). Thanks for your time :)

Hi, would it possible for someone to provide the Wavelets.jl code that recreates the example shown at the bottom here, the time-frequency analysis they show ?

Can someone explain what is needed here please?
I am already passing a float variable of which all elements are already in decimal points.

this statement wpt(x, wt, maketree(x)) return the following error

ERROR: DomainError with -1:
Cannot raise an integer x to a negative power -1.
Make x or -1 a float by adding a zero decimal (e.g., 2.0^-1 or 2^-1.0 instead of 2^-1), or write 1/x^1, float(x)^-1, x^float(-1) or (x//1)^-1

Thank you!