Method and Apparatus for Compressive Imaging Device
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example 1
Still Image Acquisition
[0070] For an imaging experiment, we displayed a printout of the letter “R” in front of the camera; FIG. 2(a) shows the printout. For acquisition and reconstruction, we use an imaging resolution of N=64×64=4096. Since our test image is piecewise constant (with sharp edges) it can be sparsely represented in the wavelet domain. FIGS. 2(b) and 2(c) show the best K-term Haar wavelet approximation of the idealized image in FIG. 2(a) with K=205 and 409, respectively. Using M=819 and 1,638 measurements (roughly 4× the K used in (b) and (c)), we reconstructed the images shown in FIGS. 2(e) and 2(f) using the Dantzig Selector (see Candès, E., Tao, T., “The Dantzig selector: Statistical estimation when p is much larger than n,” (2005) Preprint), a robust scheme for CS reconstruction. In all cases Haar wavelets were used for approximation or reconstruction. This preliminary embodiment confirms the feasibility of the CI approach; resolution of minor calibration and noise...
example 2
Video Simulation
[0071] To demonstrate the potential for applications in video encoding, we present a series of simulations for video measurement / reconstruction. FIG. 3(a) shows a single frame taken from our F=64 frame video sequence that consists of P=64×64 images; in total the video contains N=FP=262,144 3D voxels. The video shows a disk moving from top to bottom and growing from small to large. We measure this video sequence using a total of M measurements, either 2D random measurements (with M / F measurements / frame) or 3D random measurements. (For the 2D measurements, we make the simplifying assumption that the image remains constant across all snapshots within a given frame.) To reconstruct the video from these measurements we compare two approaches: 2D frame-by-frame reconstruction using 2D wavelets as a sparsity-inducing basis and 3D joint reconstruction using 3D wavelets as a sparsity-inducing basis.
[0072]FIG. 3 shows Matching Pursuit reconstruction results using M=20,000 (t...
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