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Signal processing’s free lunch The accurate recovery of undersampled signals

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It’s not really free It’s reduced price You don’t pay for what you don’t need

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Nyquist-Shannon sampling We need to sample at twice the bandwidth Expensive to gather and store all this data We end up compressing it anyway

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Compressed Sensing Sample your signal in its compressed form Only gather what you need How do we do this?

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It’s linear algebra Represent measuring as underdetermined system Sampling matrix * full signal = short measurement

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How is this possible to solve? Either 0 or ∞ solutions We know there’s a solution We can get the solution

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What is this magic?

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There’s a catch Measuring device and signal must be incoherent Signals we measure are structured Randomness is not Random measuring works best

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How it’s done in Matlab

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Example in Matlab A 1024-point long signal with 32 nonzero coefficients 256 measurements collected Undersampled by a factor 4

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The Code A = randn(256,1024); x0 = zeros(1024,1); for i = 0:32; x0(randi(1024,1)) = randn(1); end b = A*x0; xGuess = A\b; xSolved = l1eq_pd(xGuess, A, [], b);

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The result

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Not just time domain Frequency domain sampling possible Apply basis transform Difficult to do in Matlab

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The End Questions?

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