anchor.diff:  \mathcal{T}(f)(\ell) = \int_{\ell} f(x) dx  \quad \ell \text{ is a line in } \mathbb{R}^2
   +++++++++++++++++
   
  -The main complication here is that we have a global relationship between signal and data, where two widely separated points in an image can both influence a point in data space. Because of this, inversion is no longer an (approximately) local problem as in image processing, but is a global problem.
  +The main complication here is that we have a global relationship between signal and data, where two widely separated points in an image can both influence a point in data space. And since the forward model is global, so is the inverse problem.
   
   
  
positive.code: 
  = Learning to reconstruct
  
  If I gave you this data:
  
  image::mayo_convolved.png[mayo_convolved]
  
  would you be able to tell that it was generated from this object?
  
  image:mayo_phantom.png[mayo_phantom]
  
  Perhaps not, but we can teach a computer to do it.
  
  == An introduction to inverse problems
  
  
negative.code: g = \mathcal{T}(f) + noise
  +++++++++++++++++
  
  where stem:[g] is our measured data and stem:[f] is the parameters (signal) we want to reconstruct. These are connected through the _forward model_ stem:[\mathcal{T}], which describes how some set of parameters gives rise to an observation.
  
  Several classical image processing problems can be cast into this form, including denoising, inpainting, deconvolution and superresolution. But it is also a good model for more complicated modalities such as Computed Tomography (CT), Magnetic Resonance Imaging (MRI), etc.
  
  