1. A method, comprising: obtaining an input image comprising a plurality of separate microimages of an image of a scene, each of the microimages having a plurality of blocks of pixels; for each of the plurality of blocks of pixels, applying a random selection technique to randomly select one pixel from the block; and applying a rendering technique that uses the randomly selected pixels to render an output image of the scene from the plurality of separate microimages, the applying including, for each point on an image plane of the output image: determining a line of projection through the microimages in optical phase space according to a current point on the image plane and an angle of projection determined from a current depth of focus; and for each microimage intersected by the line of projection, applying a sampling kernel centered at an intersection point of the line of projection with the microimage to sample values from pixels of the microimage covered by the sampling kernel, the values only being sampled from the randomly selected pixels in the microimage by the sampling kernel, and for a given point on the image plane of the output image, pixel values from at least one of the microimages intersected by the respective line of projection not being sampled when the sampling kernel does not cover at least one of the randomly selected pixels in said at least one of the microimages.