Changes

The integral is therefore

The integral is therefore

<math>\int{dti} \int{f(x_i,t_i)g(\Delta \mathbf{x}, \Delta t) dx_i dy_i}</math>  

<math>\int{dt_i} \int{f(x_i,t_i)g(\Delta \mathbf{x}, \Delta t) dx_i dy_i}</math>  

We know that  

We know that  

This is a complicated equation, but it can be solved for G. Once G is calculated, we can apply an inverse Fourier transform and find g; we can then plug this into

This is a complicated equation, but it can be solved for G. Once G is calculated, we can apply an inverse Fourier transform and find g; we can then plug this into

<math>\int{dti} \int{f(x_i,t_i)g(\Delta x, \Delta t) dx_i dy_i}</math>  

<math>\int{dt_i} \int{f(x_i,t_i)g(\Delta x, \Delta t) dx_i dy_i}</math>  

and calculate the effects of the spherical wavelets.

and calculate the effects of the spherical wavelets.