Compressed Sensing: Compressive Coded Aperture Superresolution Image Reconstruction, TOMBO, CASSI

It's Friday and you thought that you'd go home tonight being bored and all. Too bad, you started reading this entry. The good stuff just came out from the DISP group at Duke and other researchers working with them.

First and foremost, Roummel Marcia and Rebecca Willett introduce us to Compressive Coded Aperture Superresolution Image Reconstruction. It was presented at ICASSP last week. The abstract reads:

Recent work in the emerging field of compressive sensing indicates that, when feasible, judicious selection of the type of distortion induced by measurement systems may dramatically improve our ability to perform reconstruction. The basic idea of this theory is that when the signal of interest is very sparse (i.e., zero-valued at most locations) or compressible, relatively few incoherent observations are necessary to reconstruct the most significant non-zero signal components. However, applying this theory to practical imaging systems is challenging in the face of several measurement system constraints. This paper describes the design of coded aperture masks for superresolution image reconstruction from a single, low-resolution, noisy observation image. Based upon recent theoretical work on Toeplitz structured matrices for compressive sensing, the proposed masks are fast and memory-efficient to compute. Simulations demonstrate the effectiveness of these masks in several different settings.

There is a good explanation of Coded Aperture Imaging (a subject covered before here, here and here), they then make a very illuminating statement on MURAs and then continue with how compressed sensing is literally changing the hardware (in particular masks) but notice:

However, there currently exist few guiding principles for designing coded aperture masks for nonlinear reconstruction methods.

and then they get on to

extend these results [on Toeplitz matrices mentioned here] to pseudo-circulant matrices and use them to motivate our mask design.

The conclusion state:

This paper has demonstrated that coded apertures designed to meet the Restricted Isometry Property [7] can improve our ability to perform superresolution image reconstruction from noisy, low resolution observations. In particular, building from the theory of RIPs for Toeplitz-structured matrices for compressive sensing [10], we establish a method for generating coded aperture masks in both the conventional coded aperture setting and a Fourier imaging setting; these random masks can be shown to result in an observation matrix which, with high probability, satisfies the RIP. Furthermore, simulations demonstrate that these masks combined with l2 - l1 minimization reconstruction methods yield superresolution reconstructions with crisper edges and improved feature resolution over reconstructions
achieve without the benefit of coded apertures.

A very good paper to ponder over the week-end.

Mohan Shankar, Rebecca Willett, Nikos Pitsianis, Timothy Schulz, Robert Gibbons, Robert Te Kolste, J. Carriere, C. Chen, D. Prather, David Brady write about TOMBO: Thin infrared imaging systems through multi-channel sampling.

The abstract reads:

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3mmand achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.

We talked about this article of Ashwin Wagadarikar, Renu John, Rebecca Willett, and David Brady before but I never put the abstract on. Here it is: Single disperser design for coded aperture snapshot spectral imaging,

We present a single disperser spectral imager that exploits recent theoretical work in the area of compressed sensing to achieve snapshot spectral imaging. An experimental prototype is used to capture the spatiospectral information of a scene that consists of two balls illuminated by different light sources. An iterative algorithm is used to reconstruct the data cube. The average spectral resolution is 3.6 nm per spectral channel. The accuracy of the instrument is demonstrated by comparison of the spectra acquired with the proposed system with the spectra acquired by a nonimaging reference spectrometer.

And now, I am impatiently waiting for these two papers:

• Compressive coded aperture video reconstruction, Roummel F. Marcia and Rebecca M. Willett, Submitted to 2008 European Signal Processing Conference (EUSIPCO).
• Fast disambiguation of superimposed images for increased field of view, Roummel F. Marcia, Changsoon Kim, Jungsang Kim, David Brady, and Rebecca M. Willett, Submitted to 2008 IEEE International Conference on Image Processing (ICIP).