Atrous Wavelet transform or HDR wavelet transform

[Jules]

Hi

I understand the wavelet in the sense of layers of increasing structure size. I use HDR frequently but I would like to understand more about the differences between Atrous and HDR. Do they carry out the same alterations but using different algorithms?

Or am I being a bit thick?

Regards

Julian

[Philip de Louraille]

One is used more to eliminate noise and "sharpen" features (HDRW) , the other to *isolate* structures of certain pixel sizes (À trous...) At least, this is how I use them.

[sleshin]

These two tools, ATW and HDRW, reflect PI's core paradigm, a multiscaled approach to astrophoto image processing. With the ATW tool you can enhance/sharpen structures by increasing Bias or you can deemphasize/blur structures by decreasing Bias. Another important function addressed with this tool is noise reduction as was elegantly explained by Juan in a recent post. Each of these effects can be applied to structures of various scale depending on which layer/layers one chooses to work on. The HDRW tool compresses the dynamic range but rather than compressing the range of the whole image it allows one more control by letting us choose which layers are included in the compression. This of course can serve to reveal small scale structures that were otherwise hidden which because of the resulting enhanced contrast certainly makes the image seem sharper. But I don't think HDRW is a sharpening tool per-say.

This is my meager and oversimplified understanding of these two tools. I may well be way off base and if so hopefully others will chime in with comments.

Steve

[Jules]

One is used more to eliminate noise and "sharpen" features (HDRW) , the other to *isolate* structures of certain pixel sizes (À trous...) At least, this is how I use them.

Philip

Thank you for your reply. The confusing thing with Atrous for me is the fact (as I understand it) that you can noise reduce each layer/ wavelet.

Why would you want to do that to individual layers? Isn't noise a function of the whole image rather than individual layers?

[Jules]

Steve

It is always very informative when you reply to one of my posts, thanks!

When would I want to use Atrous instead of HDR?

I use ACDNR for noise reduction after an applying HDR after a histogram transformation. Then I read that Atrous is a more sophisticated version of ACDNR and should be used in the linear phase?

Regards

Julian

[zvrastil]

Hi Julian,

noise has scale as well as the rest of the image. Typically, noise is small-scale so it appears only in first few layers. Try to make a small preview, taking only background. Then, apply ExtractWaveletLayers script to it. I will create several new images, one for each layer. You'll see lot of noise in layers 1 and 2 and less and less in higher layers. The beauty of using ATWT for noise reduction is, that you can control the amount of noise reduction per layer. Most astronomical images are oversampled (your camera has better resolution than your lens) and there's little information in layer 1 and 2. So, you can apply strong and aggressive noise reduction parameters to these layers and less aggressive noise reduction to higher layers to protect image structures.

regards, Zbynek

[Jules]

Hi Julian,

noise has scale as well as the rest of the image. Typically, noise is small-scale so it appears only in first few layers. Try to make a small preview, taking only background. Then, apply ExtractWaveletLayers script to it. I will create several new images, one for each layer. You'll see lot of noise in layers 1 and 2 and less and less in higher layers. The beauty of using ATWT for noise reduction is, that you can control the amount of noise reduction per layer. Most astronomical images are oversampled (your camera has better resolution than your lens) and there's little information in layer 1 and 2. So, you can apply strong and aggressive noise reduction parameters to these layers and less aggressive noise reduction to higher layers to protect image structures.


regards, Zbynek

Hi Zbynek

That is very well explained, thank you. I shall try out what you have described above.

Regards

Julian

[sleshin]

Julian,

In case you missed it, here is Juan's excellent tutorial on using ATW for noise reduction.

http://pixinsight.com/forum/index.php?topic=3184.msg21961#msg21961

Steve

[Jules]

Steve

Thanks I will have a look at that.

Regards

Julian

[Jules]

Hi Julian,

noise has scale as well as the rest of the image. Typically, noise is small-scale so it appears only in first few layers. Try to make a small preview, taking only background. Then, apply ExtractWaveletLayers script to it. I will create several new images, one for each layer. You'll see lot of noise in layers 1 and 2 and less and less in higher layers. The beauty of using ATWT for noise reduction is, that you can control the amount of noise reduction per layer. Most astronomical images are oversampled (your camera has better resolution than your lens) and there's little information in layer 1 and 2. So, you can apply strong and aggressive noise reduction parameters to these layers and less aggressive noise reduction to higher layers to protect image structures.

regards, Zbynek

Zbynek

Thats a very useful script, it produces a  layer 0 which does contain some small detail though. I have noticed with this script and the ATWT there is a residual layer. Is this everything not in the previous layers?

Regards

Julian

[Jules]

Julian,

In case you missed it, here is Juan's excellent tutorial on using ATW for noise reduction.

http://pixinsight.com/forum/index.php?topic=3184.msg21961#msg21961

Steve

Steve

I have just worked through my own data using this tutorial, I was astounded with the results.

Regards

Julian

[zvrastil]

Thats a very useful script, it produces a  layer 0 which does contain some small detail though. I have noticed with this script and the ATWT there is a residual layer. Is this everything not in the previous layers?

Hi Julian,

yes, there's almost always some information even in layer 0, but still the noise reduction here can be much stronger. Residual layer indeed contains what is not in extracted layers. In ATWT, this layer is denoted R. You can thinkof it like sum of all higher layers up to infinity (or size of the image). This layer is necessary to perform inverse transformation (from wavelet layers back to image).

Zbynek

[Jules]

Zbynek

I reworked though some of my images using ATWT and the results were impressive. Thank you for spending the time!

Regards

Julian