# Methodology for Extracting Information from "Random" Measurements

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Connexions module: m13137 1 Methodology for Extracting Information from "Random" Measurements ∗ Heather Johnston Siddharth Gupta Veena Padmanabhan Grant Lee This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License † Abstract Our approach for detecting the speed of a known object. 1 Simulating Compressed Sensing Because compressed sensing cameras are not yet availiable, we used a Matlab routine written by Ilan Good- man to simulate CS measurements from a standard pixel image file [1]. Only the compressed sensing mea- surements are passed into our suite of calculation programs which run exactly as if the CS measurements came from a hardware-implemented CS camera. To implement compressed sensing on an image (matrix) according to the definition, a random matrix the same size of the image is generated. The projection (inner product) of the image onto the random basis matrix gives a single compressed sensing measurement. This is repeated with different (fixed) random matricies until the desired compressed sensing resolution is achieved. This is computationally intensive and so a different approach is used in practice to simulate our data: first, every pixel of the image is randomly mapped to a different location to randomize the image. Next, the DCT (discrete cosine transform) is taken on the randomized image. This process of randomization and projection is equivalent to projection onto a random basis [1]. 2 Random, On Average We exploited two key facts about compressed sensing on a random basis to calculate speed: 1) The average value of the elements of the random basis used is 1. 2) On a given image, a fixed random basis yields the same projections every time it is used. ∗ Version 1.2: Dec 23, 2005 1:16 pm US/Central † http://creativecommons.org/licenses/by/2.0/ http://cnx.org/content/m13137/1.2/ Connexions module: m13137 2 While seemingly trivial, this basic data allows us t

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