Image Reconstruction from Sparsely Sampled Data

At a Glance

Researchers at Colorado State University have developed an innovative method for inpainting and reconstructing sparsely-sampled images based on iterative cycling between the real space and a transform domain. The novel part of this technology is the gradual relaxing of the sparsity constraint in the transform domain with each iteration, resulting in a more accurate initial guess in unsampled gaps. This algorithm is effective for processing any 2D or 3D (image) data that is sparsely sampled.


Efficient and effective methods to fill in gaps in an image have numerous applications. With medical imaging there is value in being able to speed up data acquisition by collecting fewer data points, or exposing a patient to less radiation, but there is still a need for a high-quality image. Shorter sampling time can also enable image capture of fast-moving objects such as a beating heart or neuronal activations. Similar principles and benefits apply for other microscope-based imaging for research. Art restoration may need to examine a damaged area and extrapolate what was previously in that part of the image. Another artistic application is image object removal, such as to remove a fence from an image and fill in the space where the fence used to be. This new method for image reconstruction is versatile in its application and could provide many benefits across multiple fields of use.


This image reconstruction technique was developed to address an imaging scan pattern that achieved a large field-of-view at the expense of scan pattern distortion and a sparsely sampled image. To mitigate these problems, the acquired samples were binned into a spatial grid and a fast iterative Fourier-filtering reconstruction method (FIFFR) is used to fill in the missing data. The method was tested on an image where the true image was known and outperformed a related algorithm for reconstructing images in a side-by-side comparison. FIFFR outperformed in terms of speed and the quality of the final reconstruction. Additionally, when applied to the experimentally gathered data, FIFFR doubled the usable field of view in post processing of the image.


  • Ability to produce more accurate initial guesses in larger unsampled data gaps, leading to superior overall results
  • Applicability with any 2D or 3D (image) data that is sparsely sampled, making it highly versatile
  • Physical constraints reduce chances of non-physical constraints introducing artifacts
  • High quality images with faster reconstruction and a larger usable field of view for sparsely sampling imaging devices


  • Medical Imaging: The technology can be used to lower overall radiation exposure to patients when ionizing radiation is concerned, while still providing high quality images
  • Art Restoration: It can help restore artworks with missing data points
  • Targeted Object Removal: Offers the possibility of removing certain elements from an image and filling in the space where the element used to be
Last Updated: August 2023

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Cameron Coleal
Jesse Wilson

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