Non-Linear regression in Julia

Why Julia ?
I gave a talk yesterday at the Tucson Python MeetUp about how Julia and Python can be used to analyze medical images. It turns out that for a simple processing task of calculating a T1 map of a lemon Julia is 10 times faster than Python and ~635 times faster than Matlab. Besides speed, Julia offers other great features:

1. General purpose programming language
2. Designed for scientific computing
3. Aims to solve the two language issue
4. Just-in-time compiling
5. Great Packaging system
6. Call C / C++ directly
7. Call Python directly
8. Metaprogramming
9. Multiple Dispatch

How to perform non-linear regression in Julia? 
The objective of this analysis was to estimate the T1 time (seconds) for all pixels in the MRI of a lime. The assumed function is an exponential recovery of the form y = 1-exp(- x / T1). The Julia and Python notebooks are here.

I applied a similar strategy to calculate the map below using Python and Julia_vs_Python. For details go here]