The compressive imaging field is starting to mature. Case in point the following papers that seem to use similar ideas even though they come from different backgrounds. In the first paper, this is the first time we see the use of compressed sensing in the time dimension with Compressive Coded Aperture Video Reconstruction by Roummel Marcia and Rebecca Willett. The abstract reads:
This paper concerns compressive sensing methods for overcoming the pixel-limited resolution of digital video imaging systems. Recent developments in coded aperture mask designs have led to the reconstruction of static images from a single, low-resolution, noisy observation image. Our methods apply these coded mask designs to each video frame and use compressive sensing optimization techniques for enhanced resolution digital video recovery. We demonstrate that further improvements can be attained by solving for multiple frames simultaneously, even when the total computation time budget is held fixed.
They use the same method for designing the coded aperture as they did in their previous important paper mentioned here. The interesting aspect of their study is their use of the redundancy of the different frames of a movie. In one of their schemes, they use a similar approach as the one shown in the last slide of Yin Zhang's presentation at Texas A&M L1 meeting ( Enhanced Compressive Sensing and More, Yin Zhang ) whereby the solution of the previous frame is used as a guess in the search for the next frame. Since the differences between two sparse frames is very sparse, the expectation is that the time spent by the nonlinear solver for the second frame will be faster with the prior knowledge of the previous frame. As they mention in their conclusions:
The improvement in accuracy only abates when the size of the problem is such that only a very small number of reconstruction iterations can be run within the allotted time. All the approaches presented in this paper outperform frame-wise upsampling or interpolation. The results presented in this paper have an alternative interpretation. If the desired accuracy is held fixed, then the amount of processing time required to achieve that accuracy is in general smaller when the block size (the number of frames processed simultaneously) is larger. This somewhat counterintuitive result demonstrates the importance of exploiting inter-frame correlations, even when it means increasing the size of the optimization problem.
http://www.ee.duke.edu/nislab/eusipco2008. The study uses GPSR.
Another group at Ben Gurion University seems to also seek ways to produce Compressed Sensing Imaging architectures. Here are four papers from that group:
Single-shot compressive imaging by Adrian Stern, Yair Rivenson and Bahram Javidi. The abstract reads:
We present a method to capture directly a compressed version of an object’s image. The compression is accomplished by optical means with a single exposure. For objects that have sparse representation in some known domain (e.g. Fourier or wavelet) the novel imaging systems has larger effective space-bandwidth-product than conventional imaging systems. This implies, for example, that more object pixels may be reconstructed and visualized than the number of pixels of the image sensor.
The "Phase mask with correlation length ρ is attached to a lens with diameter D." The article defines how that correlation length must be bounded in order to produce a satisfactory random measurement.
Optically compressed image sensing using random aperture coding by Adrian Stern, Yair Rivenson and Bahram Javidi. The abstract reads:
The common approach in digital imaging today is to capture as many pixels as possible and later to compress the captured image by digital means. The recently introduced theory of compressed sensing provides the mathematical foundation necessary to change the order of these operations, that is, to compress the information before it is captured. In this paper we present an optical implementation of compressed sensing. With this method a compressed version of an object's image is captured directly. The compression is accomplished by optical means with a single exposure. One implication of this imaging approach is that the effective space - bandwidth - product of the imaging system is larger than that of conventional imaging systems. This implies, for example, that more object pixels may be reconstructed and visualized than the number of pixels of the image sensor.
It uses the same architecture as the one previously shown above:
The paper use of StOMP for reconstruction.
Random projections imaging with extended space-bandwidth product by Adrian Stern and Bahram Javidi. The abstract reads:
We propose a novel approach to imaging that is not based on traditional optical imaging architecture. With the new approach the image is reconstructed and visualized from random projections of the input object. The random projections are implemented within a single exposure by using a random phase mask which can be placed on a lens. For objects that have sparse representation in some known domain (eg. Fourier or wavelet) the novel imaging systems has larger effective space-bandwidth product than conventional imaging systems. This implies, for example, that more object pixels may be reconstructed and visualized than the number of pixels of the image sensor. We present simulation results on the utility of the new approach. The proposed approach can have broad applications in efficient imaging capture, visualization, and display given ever increasing demands for larger and higher resolution images, faster image communications, and multi dimensional image communications such as 3D TV and display.
This Letter presents a new approach for imaging using a linear (vector) sensor. It exploits the fact that visual information within common human intelligible images may be compressed within only a partial set of radial strips of its Fourier domain. We present two imaging schemes, one coherent and the other incoherent, that capture the partial set of radial strips of the object Fourier domain. Two main advantages of the new approach are that the image is captured directly in a compressed form and that the acquisition time is shorter compared with conventional scanning imaging systems.
This is the compressed sensing version of some sampling schemes featured in Dappled Photography: Mask Enhanced Cameras for Heterodyned Light Fields and Coded Aperture Refocusing by Ashok Veeraraghavan, Ramesh Raskar, Amit Agrawal, Ankit Mohan and Jack Tumblin.
Credit: NASA. JPL-Caltech, University of Arizona. First print on Mars by the Phoenix digging arm.
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