Using of Discrete Orthogonal Transforms for Convolution [pdf]

Using of Discrete Orthogonal Transforms for Convolution [pdf](iris.elf.stuba.sk)

29 points by alecdibble 10 years ago | 6 comments

thearn4 10 years ago |

I had a large interest in discrete convolution operations a few years ago, particularly in application to digital image processing. Two papers that I published may be of interest to those here:

[A paper that as a lemma demonstrates the influence of boundary conditions on the use of discrete orthogonal transformations for fast convolution operations] https://scholar.google.com/citations?view_op=view_citation&h...

[accelerating convolution operations when a matrix factorization (SVD, DCT for jpeg, etc.) is already available]

https://scholar.google.com/citations?view_op=view_citation&h...

tacos 10 years ago | |

Second paper in particular is pretty fascinating. I'm sure you see the parallels to convolutional neural networks. Thanks for posting.

tacos 10 years ago |

I'm pretty sure this paper was generated by a bot. Aside from phrases like "The evaluation of the WHTs product needs only real multiplications by +1 or 1" I see phrases culled from expired patents. Googling pulls up a more interesting paper from the 70s. This is weird.

loxias 10 years ago | |

With the disclaimer that I have not worked through proofs of what is asserted, I read through the paper and it makes sense to me. Though it does have plenty of editing mistakes, which are somewhat distracting.

The paper might very well be produced by cribbing form other sources, I couldn't say -- but the central idea, that a convolution can be computed in some cases by methods with lower computational complexity than the product of the DFT, is interesting, I look forward to implementing it. :)

(And yeah, the product of two WHT transformed sequences does only need multiplication by +1 or -1...)

tacos 10 years ago | | |

Mostly I'm confused why a nearly 15 year old, poorly-written journal article appeared on HN today with no comments. And I wasn't kidding: I'm familiar with the state of the art and reading it from the title on down it really felt like something a bot glued together.

There was some buzz around convolution methods in the late 90s. Lake DSP had a notable patent which actually inspired some research. Most if not all of these methods now exist in Matlab and scipy.signal.convolve with far better documentation.

But I grow weary of random, crappy HN links like this one that really feel like some enthusiast did a Google search but didn't even read the paper.