Figure 1:
**Effect of signal prior on multiplexing gain of focal sweep [3,4]:** We show the multiplexing gain of focal sweep over impulse imaging (a conventional camera with stopped down aperture) at different photon to read noise ratios J/σ_{r}^{2}. The photon to read noise ratio is related to illumination level and camera specifications. In the extended x-axis, corresponding to different values of J/σ_{r}^{2}, we show the light levels (in lux) for three camera types: a high end SLR, a machine vision camera (MVC) and a smartphone camera (SPC). As shown by Cossairt et al. [1], without using signal priors, we get a huge multiplexing gain at low J/σ_{r}^{2}. But with a signal prior (GMM) the multiplexing gain is modest even at low J/σ_{r}^{2}. Thus, this figure clearly shows the importance of analyzing CI systems with signal priors taken into account.

');
$p->addSection('Project Description', '
Over the last decade, a number of Computational Imaging (CI) systems have been proposed for tasks such as motion deblurring, defocus deblurring and multispectral imaging. These techniques increase the amount of light reaching the sensor via multiplexing and then undo the deleterious effects of multiplexing by appropriate reconstruction algorithms. Given the widespread appeal and the considerable enthusiasm generated by these techniques, a detailed performance analysis of the benefits conferred by this approach is important.

Unfortunately, a detailed analysis of CI has proven to be a challenging problem because performance depends equally on three components: (1) the optical multiplexing, (2) the noise characteristics of the sensor, and (3) the reconstruction algorithm which typically uses signal priors. A few recent papers [1,2] have performed analysis taking multiplexing and noise characteristics into account. However, analysis of CI systems under state-of-the-art reconstruction algorithms, most of which exploit signal prior models, has proven to be unwieldy. We present a comprehensive analysis framework incorporating all three components.

In order to perform this analysis, we model the signal priors using a Gaussian Mixture Model (GMM). A GMM prior confers two unique characteristics. Firstly, GMM satisfies the universal approximation property which says that any prior density function can be approximated to any fidelity using a GMM with appropriate number of mixtures. Secondly, a GMM prior lends itself to analytical tractability allowing us to derive simple expressions for the \'minimum mean square error\' (MMSE) which we use as a metric to characterize the performance of CI systems. We use our framework to analyze several previously proposed CI techniques (focal sweep [3,4], flutter shutter [5], parabolic exposure [6], etc.), giving conclusive answer to the question: \'How much performance gain is due to use of a signal prior and how much is due to multiplexing?\' Our analysis also clearly shows that multiplexing provides significant performance gains above and beyond the gains obtained due to use of signal priors.

'); //$p->printSections(); // Add publications here. You can use either the publication number, or the full title //$p->addPublication(321); //$p->printPublications(); $p->addSection('Publications', '"A Framework for Analysis of Computational Imaging Systems: Role of Signal Prior, Sensor Noise and Multiplexing,"

K. Mitra, O. Cossairt, A. Veeraraghavan,

arXiv:1308.1981,

PAMI, 2014

[PDF]

"Performance Bounds for Computational Imaging," (Invited)

O. Cossairt, M. Gupta, K. Mitra, A. Veeraraghavan,

Imaging and Applied Optics Technical Papers,

OSA, 2013.

[PDF]

"Performance Limits for Computational Photography," (Invited)

O. Cossairt, K. Mitra, A. Veeraraghavan,

International Workshop on Advanced Optical Imaging and Metrology,

Springer, 2013.

[PDF]

' ); $p->addSection('Presentations', '"To Denoise or Deblur: Parameter Optimization for Imaging Systems,"

K. Mitra, O. Cossairt and A. Veeraraghavan,

SPIE Electronic Imaging Conference, 2014

[PDF]

"Performance Bounds for Computational Imaging,"

O. Cossairt

Computational Optical Sensing and Imaging Conference, June 2013.

[PDF]

"When Does Computational Imaging Improve Performance?,"

O. Cossairt

CVPR Workshop on Computational Cameras and Displays, June 2013.

[PDF]

"Compressive Imaging,"

A. Veeraraghavan

CVPR Workshop on Computational Cameras and Displays, June 2013.

' ); $p->printSections(); // Add images here. Args are (url to image, url to thumbnail, title, description) $p->addImage("images/illumToNumPhotons.png", "images/illumToNumPhotons_thumb.png", "Image formation and noise model", "Follow the convention adopted by Cossairt et al. [1], we define a conventional camera as an impulse imaging system which measures the desired signal directly (e.g. without blur). CI performance is then compared against the impulse imaging system. Noise is related to the lighting level, scene properties and sensor characteristics. To calculate the photon noise in our experiments, we assume an average scene reflectivity of R=0.5 and sensor quantum efficiency of q=0.5, aperture setting of F/11 and exposure time of t=6 milliseconds. We choose three different example cameras that span the a wide range of consumer imaging devices: 1) a high end SLR camera, 2) a machine vision camera (MVC) and 3) a smartphone camera (SPC). For each of these example camera types, we choose parameters that are typical in the marketplace today: sensor pixel size: δ"Performance Limits for Computational Photography,"

O. Cossairt

Fringe Conference, September 2013.

- [1] O. Cossairt, M. Gupta, and S.K. Nayar,
*When Does Computational Imaging Improve Performance?,*IEEE Transactions on Image Processing, 2012. - [2] N. Ratner, Y. Schechner, and F. Goldberg.
*Optimal multiplexed sensing: bounds, conditions and a graph theory link.*Optics Express, 2007. - [3] G. Hausler.
*A method to increase the depth of focus by two step image processing.*Optics Communications, 1972. - [4] H. Nagahara, S. Kuthirummal, C. Zhou, and S. Nayar.
*Flexible Depth of Field Photography.*In ECCV, 2008. - [5] R. Raskar, A. Agrawal, and J. Tumblin.
*Coded exposure photography: motion deblurring using fluttered shutter.*In SIGGRAPH, 2006. - [6] A. Levin, P. Sand, T. Cho, F. Durand, and W. Freeman.
*Motion-invariant photography.*In SIGGRAPH, 2008. - [7] C. Zhou and S. Nayar.
*What are good apertures for defocus deblurring?*In ICCP, 2009. - [8] A. Levin, R. Fergus, F. Durand, and W. T. Freeman.
*Image and depth from a conventional camera with a coded aperture.*In SIGGRAPH, 2007. - [9] E. R. Dowski and T. W. Cathey.
*Extended depth of field through wave-front coding.*Applied Optics, 1995.