[MUSIK]

welcome everybody to pattern recognition this

week as you may have noticed I am not professor Hornegger my name is

Andreas Maier and I am going to hold the lecture this week because professor

Hornegger is on a business trip so he won't be

in this week so I also work at the pattern

recognition lab I mostly do image reconstruction segmentation topics and

this is all related to pattern recognition and I used to be an employee of

a smaller mid sized company very close to here until this October and

then a changed back from industry to here you may guess what company that was okay so

you guys have been talking about pattern

recognition and what what stuff have you

been talking about where did you stop

okay do you always contribute that much

to the lecture come on I need some help here it's not

just me talking to a wall or to an opening and

closing door hi what's your name Franziska

have you attended the last lecture

yes who am I okay that

was mean I'm substituting professor Hornegger this week and

the last topic you intended to talk about as far as I understood was

compressed sensing did you see this slide before

you should have seen it if we go back did you see this slide you remember so here

the emphasis is L1 norm and how you can

get a sparse optimization result using the L1 norm

so why is this result sparse okay how

does how does this vector look like this optimization result so this is obviously the

point 1 0 right why is this a

sparse solution yes yes yes yes exactly so we have a 0 here this

makes this solution sparse and now we can actually apply this in compressed

sensing so we regularized linear regression or you regularized

linear regression together with professor Hornegger and now let's

assume we have fewer measurements than required to estimate

the parameter vector x so we have an underdetermined

solution so we actually can find can find many solutions here

so we can use regularization to find a specific solution and here we use

compressed sensing is the idea that we do something about the

objective function to get to a specific solution and here we

we exploit if we know about something we measure that its

sparse in a certain representation now the example we've

just seen was a very academic one but you can find

that for example in medical imaging if you look at an angiogram

who knows what an angiogram is by the way have you heard about that did you do you know what okay

so this is an is an X-ray projection technique and the idea is that you want to visualize

only vessels and the idea is that you do an image of the patient and

you just take a usual X-ray projection and then you inject contrast agent into

the vessels and then you take a second projection and you subtract those

two and all that remains is the image of the vessels because

all that has changed is the information in the vessels and usually

you get some some kind of projection which is the result of