how to specify number of modes/frequencies? about tensorflow-nufft

[jmontalt]

Hi @samaktbo,

1. The number of modes can be specified using the argument grid_shape. It maps exactly to the nmodes argument of FINUFFT.
2. No, the type-1 and type-2 transforms match those of FINUFFT, as well as the original naming from "Dutt A, Rokhlin V. Fast Fourier transforms for nonequispaced data. SIAM Journal on Scientific computing. 1993 Nov;14(6):1368-93". This is specified on the docs. Can I ask what confused you in this regard?

[samaktbo]

Oh! Thanks for the clarification, I ended up figuring out that probably the number of modes can be inferred form the grid shape. I think what was confusing me is that whenever I heard grid, I was thinking non-uniform points real-valued points, I only realized later that the integer lattice is also a grid. I think this is also partly why I thought the roles were switched.

The main reason I thought there had been a switch is because the example that is given (the MRI example) is doing the opposite of what I wanted to do (@davidwhogg helped me see this): in my project the number of modes is always uniform, but the points of evaluation (pixels) are non-uniform but it seems like in that example, the pixels are sampled uniformly but the desire is to have non-uniform modes. Would you say that is accurate?

[jmontalt]

Indeed, that is correct. In MRI, we often measure spatial frequencies in a set of non-uniform points, and then we need to evaluate the NUDFT to obtain an image (on a grid of pixels, naturally).

It is useful to remember that the transform_type only indicates whether you're going from uniform to non-uniform ('type_2') or non-uniform to uniform ('type_1'), but it says nothing about the direction of the transform in terms of signal/frequency domains. That is controlled independently by the fft_direction (use 'forward' for signal -> frequency and 'backward' for frequency -> signal).

When I have a chance I will try to add a couple more examples to help clarify this.