Boyd Convex Optimization book - SFU Wiki
Boyd Convex Optimization book - SFU Wiki
Boyd Convex Optimization book - SFU Wiki
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316 6 Approximation and fitting<br />
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Figure 6.12 Three quadratically smoothed signals ˆx. The top one corresponds<br />
to ‖ˆx − x cor‖ 2 = 10, the middle one to ‖ˆx − x cor‖ 2 = 7, and the<br />
bottom one to ‖ˆx − x cor‖ 2 = 4. The top one greatly reduces the noise, but<br />
also excessively smooths out the rapid variations in the signal. The bottom<br />
smoothed signal does not give enough noise reduction, and still smooths out<br />
the rapid variations in the original signal. The middle smoothed signal gives<br />
the best compromise, but still smooths out the rapid variations.<br />
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Figure 6.13 Optimal trade-off curve between ‖Dˆx‖ 1 and ‖ˆx − x cor‖ 2.
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