An electronic device may have a digital image sensor for capturing an image and may have storage and processing circuitry for processing the image to produce a corresponding enhanced depth-of-field image. Multiple image areas, within a given image may be processed. As each image area is processed, a signal-to-noise ratio may be computed. A kernel parameter characteristic curve may be used to select values to be used for kernel parameters for each image area based on the computed signal-to-noise ratio for that image area. Kernels may be generated for each image area and the generated kernels may be convolved with their respective image areas to modify the image areas. This allows each image area to be selectively sharpened or smoothed based on its signal-to-noise ratio. Image areas with low and high signal-to-noise ratios may be sharpened less those with moderate signal-to-noise ratios to enhance depth of field in the image.