Computational imaging

• Comment: I shall accept but please enhance the current number of sources given, as this could certainly use a larger number. SwisterTwister talk 05:23, 26 October 2017 (UTC)

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Computational Imaging is the process of indirectly forming images from measurements using algorithms that rely on a significant amount of computing. In contrast to traditional imaging, computational imaging systems involve a tight integration of the sensing system and the computation in order to form the images of interest. The ubiquitous availability of fast computing platforms (such as multi-core CPUs and GPUs), the advances in algorithms and modern sensing hardware is resulting in imaging systems with significantly enhanced capabilities. Computational Imaging systems cover a broad range of applications include computational microscopy, tomographic imaging, MRI, ultrasound imaging, computational photography, Synthetic Aperture Radar (SAR), seismic imaging etc. The integration of the sensing and the computation in computational imaging systems allows for accessing information which was otherwise not possible. For example:

• A single X-ray image does not reveal the precise location of fracture, but a CT scan which works by combining multiple X-ray images can determine the precise location of one in 3D
• A typical camera image cannot image around corners. However, by designing a set-up that involves sending fast pulses of light, recording the received signal and using a algorithm, researchers have demonstrated the first steps in building such a system.

Computational imaging systems also enable system designers to overcome some hardware limitations of optics and sensors (resolution, noise etc.) by overcoming challenges in the computing domain. Some examples of such systems include coherent diffractive imaging, coded-aperture imaging and image super-resolution.

History

Computational imaging systems span a broad range of applications. While applications such as SAR, computed tomography, seismic inversion are well known, they have undergone significant improvements (faster, higher-resolution, lower dose exposures) driven by advances in signal and image processing algorithms (including compressed sensing techniques) and faster computing platforms. Photography has evolved from purely chemical processing to now being able to capture and computationally fuse multiple digital images (computational photography) making techniques such as HDR and panoramic imaging available to most cell-phone users. Computational imaging has also seen an emergence of techniques that modify the light source incident on an object using known structure/patterns and then reconstructing an image from what is received (For example: coded-aperture imaging, super-resolution microscopy, Fourier ptychography). Advances in the development of powerful parallel computing platforms has played a vital role in being able to make advances in computational imaging.

Algorithms

While computational imaging covers a broad range of applications, the algorithms used in computational imaging systems are often related to solving a mathematical inverse problem. The algorithms are generally divided into direct inversion techniques which are often "fast" and iterative reconstruction techniques that are computationally expensive but are able to model more complex physical processes. The typical steps to design algorithms for computational imaging systems are:

1. Formulating a relationship between the measurements and the quantity to be estimated. This process requires a mathematical model for how the measurements are related to the unknown. For example: In high-dynamic range imaging, the measurements are a sequence of known exposures of the underlying area to be imaged. In an X-ray CT scan, the measurements are X-ray images of the patient obtained from several known positions of the X-ray source and detector camera with a well established relationship for X-ray propagation.
2. Choosing a metric to "invert" the measurements and reconstruct the quantity of interest. This could be a simple metric such as a least-squares difference between the measurements and the model or a more sophisticated metric based on precisely modeling the noise statistics of the detector and a model for the object of interest. This choice can be related to choosing a statistical estimator for the quantity to be reconstructed.
3. Designing fast and robust algorithms that compute the solution to Step 2. These algorithms often use techniques from mathematical optimization and mapping such methods to fast computing platforms to build practical systems.

Further Reading

Advances in the field of computational imaging research is presented in several venues including publications of SIGGRAPH and the IEEE Transactions on Computational Imaging.