Radon transform Puns

Besides Yilmaz's book, is there any other source that you would recommend to learn about Radon transform and its application on seismic data processing?

Thank you so much!

I am an undergrad who is researching the Radon transform. My focus is on the radon transform in applications like CT scans and similar imaging techniques. So far all the examples I've seen are with either generalized formulas or MatLab code. Do any of you know of any sources where the radon transform is performed by hand/simple calculator? I'm trying to understand how the Radon Transform and the unfiltered/filtered back projection algorithm would work on a simple shape of constant density such as as a solid rectangle or circle centered at the origin.
Also any sources that are easy for an undergrad to understand the basics of the radon transform and its relation to the Fourier transform.

So currently have someone else's code (people really need to work on making useful variable names and commenting). Any ways, pretty much I have a 256x256 image and am using the radon function and I am not sure how to interpret it's output.

[R,xp] = radon(I, theta) I take the max value to find the highest intensity and therefore the first line. But I am not sure which line in my image it is finding. Assuming my max value is at max_r and max_c. theta(max_c) is the angle and xp(max_r) is the x' position. How do I use these to find highlight the line it's finding?

also I know xp represents a value on x' axis. That axis is around 370 for me when my image is 265 by 256. How does that make sense?

Hello everybody,

I have a course called biomedical imaging and for a lab I need to implement a backprojector in matlab that reconstructs the original image from a sinogram.

They give me the basis of the algorithm but I don't really understand what needs to happen. Can anybody give me some explanation of what exactly needs to happen?

Thanks in advance.

From an email from the chair of the Cornell math department:

>I am sad to share that our colleague and friend Professor Robert Strichartz died yesterday, 19 December 2021, after a long illness. He was 78.
>
>Bob Strichartz earned his B.A. from Dartmouth College in 1963 and his Ph.D. from Princeton University in 1966, where he worked with Elias Stein. His thesis was entitled, Multipliers on Generalized Sobolev Spaces. He was a NATO postdoctoral fellow at Orsay from 1966-1967, and then a C.L.E. Moore Instructor at MIT from 1967 to 1969. Bob was appointed Assistant Professor of Mathematics at Cornell in 1969, Associate Professor in 1971, and Full Professor in 1977. Over the years at Cornell, he played a significant role on our Outreach Committee, Math Club Committee, and Math Majors Committee. Bob was the driving force behind our REU, he founded the Math Explorers Club that reaches local middle and high school students, and he has mentored nine PhD students and many undergraduate researchers.
>
>Bob Strichartz was an acclaimed analyst. MathSciNet has indexed 189 of his books and papers. It indicates 4,413 citations of his work. His most highly cited paper, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, has been cited 611 times. In this paper, Bob proved sharp, scale-invariant Lp estimates for solutions of dispersive partial differential equations (such as Schrödinger or wave equations) in terms of the L2 norm of their initial data. These estimates are now called Strichartz estimates in his honor. MathSciNet identifies 1206 articles and books that reference them.
>
>There is no better way to describe Strichartz’s early career, than to mention his yearlong stay in Paris. His PhD advisor Stein was also in Paris and delivered a legendary course on harmonic analysis at the University of Paris Sud (Orsay) captured in the equally famous book, Singular Integrals and Differential Properties of Functions. Bob’s thesis on spectral multipliers acting on fractional Sobolev spaces includes new descriptions of these spaces and fits perfectly with the spirit of Stein’s book.
>
>An original thinker with broad interests, Bob made influential contributions to many subjects including classical harmonic analysis (e.g. Radon transform), its application to partial differential equations (e.g., the famous Strichartz estimates concerning solutions of the wave eq

Ordinarily, I’d put this in the Quick Questions thread, but, alas, it’s not a quick question, nor is it well-known. Let p and q be distinct primes, and let f be a continuous function from the p-adic integers to the q-adic rationals (a “(p,q)-adic function”, as I call it).

I am performing analysis (specifically, (p,q)-adic Fourier analysis) with such functions. This is a rarity, so much so that even Keith Conrad asked me on mathoverflow “what’s the point” (seeing as most uses of the p-adics require much more structure (ex: analyticity) than what can be found in (p,q)-adic functions—the zeroes of which, for example, can be any closed set of p-adic integers.

Well... they come up naturally in the study of the Collatz Conjecture and the dynamics of Collatz-type maps. For classically trained analysts such as myself, as weird as p-adic analysis is, (p,q)-adic Analysis is even weirder.

For example, for a (p,q)-adic function f, the following are equivalent:

• f is continuous

• f is integrable (with respect to the q-adic-valued Haar probability measure on the p-adics)

• f is representable by an absolutely convergent Fourier series

Other oddities include the fact that there is no analogue of the classical notion of two functions being equal “almost everywhere”; two (p,q)-adic functions have the same integral if and only if they are the same, everywhere.

In my work, I’ve found a way to extend the notion of integrability to include a class of discontinuous (p,q)-adic functions that arise out of interpolating certain well-behaved rational-valued functions on the non-negative rational integers to (p,q)-adic functions, for appropriately chosen values of p and q. The idea, in short, is to treat these discontinuous functions as measures (or, rather, as the (Radon-Nikodym?) derivatives of measures). In this way, one can show that these functions admit a unique Fourier transform, even though the usual integral transform formula fails to be convergent because the integrand, in this case, is not continuous.

Playing around with the (p,q)-adic Hahn-Banach Theorem gives me an argument which would make sense in a non-Archimedean context, but which produces something very odd in the (p,q)-adic context: namely, I obtain a series formula for my (p,q)-adic function which converges to the correct value for every p-adic integer input, but with the caveat that, if the input is a non-negative rational integer, the series must be treated as converging in the usual topo

Has anyone heard of the fan theory that there is a radon leak in the office which is why the employees get weirder over time due to exposure? I think it’s one of my favorite theories because not much explains Ryan’s transformation lol

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

Alot of great jokes get posted here! However just because you have a joke, doesn't mean it's a dad joke.

THIS IS NOT ABOUT NSFW, THIS IS ABOUT LONG JOKES, BLONDE JOKES, SEXUAL JOKES, KNOCK KNOCK JOKES, POLITICAL JOKES, ETC BEING POSTED IN A DAD JOKE SUB

Try telling these sexual jokes that get posted here, to your kid and see how your spouse likes it.. if that goes well, Try telling one of your friends kid about your sex life being like Coca cola, first it was normal, than light and now zero , and see if the parents are OK with you telling their kid the "dad joke"

I'm not even referencing the NSFW, I'm saying Dad jokes are corny, and sometimes painful, not sexual

So check out r/jokes for all types of jokes

r/unclejokes for dirty jokes

r/3amjokes for real weird and alot of OC

r/cleandadjokes If your really sick of seeing not dad jokes in r/dadjokes

Punchline !

Edit: this is not a post about NSFW , This is about jokes, knock knock jokes, blonde jokes, political jokes etc being posted in a dad joke sub

Edit 2: don't touch the thermostat

Do your worst!

How the hell am I suppose to know when it’s raining in Sweden?

Ants don’t even have the concept fathers, let alone a good dad joke. Keep r/ants out of my r/dadjokes.

But no, seriously. I understand rule 7 is great to have intelligent discussion, but sometimes it feels like 1 in 10 posts here is someone getting upset about the jokes on this sub. Let the mods deal with it, they regulate the sub.

They were cooked in Greece.

I'm surprised it hasn't decade.

Two muffins are in an oven, one muffin looks at the other and says "is it just me, or is it hot in here?"

Then the other muffin says "AHH, TALKING MUFFIN!!!"

Don't you know a good pun is its own reword?

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

And now I’m cannelloni

Because she wanted to see the task manager.

But that’s comparing apples to oranges

And boy are my arms legs.

Heard they've been doing some shady business.

Now that I listen to albums, I hardly ever leave the house.

but then I remembered it was ground this morning.

Edit: Thank you guys for the awards, they're much nicer than the cardboard sleeve I've been using and reassures me that my jokes aren't stale

Edit 2: I have already been made aware that Men In Black 3 has told a version of this joke before. If the joke is not new to you, please enjoy any of the single origin puns in the comments

They’re on standbi

BamBOO!

A play on words.

My daughter, Chewbecca, not so much.

Pilot on me!!

Christopher Walken

Nothing, he was gladiator.