I have a field of voxels with different intensity values that indicate the presence of nearby objects. The default value of a voxel is zero. If an object is at the center of a voxel then the intensity is increased by 1. Objects father from the center of a voxel result in less activation. The activation decreases linearly to 0 when the object is two voxel widths away. After this, the activation remains at zero: There are no negative activations. A voxel is affected by all nearby objects and its intensity always matches the sum of the activations.
I know the number of objects in the field and there is a theoretical limit to how close the objects can be together and thus the number of objects near any given voxel.
What would be a good way to find the locations (or possible locations) of all objects, given the intensity values of the voxels?
Answers can include imperfect solutions. For example, while more "pure" solutions are preferred, "Train a neural network to do it." would be an acceptable suggestion.
Here is a 2D example of how the intensities are computed. There are four objects in this field. Green color represents the activation. 2D pixels activated this way by four objects
