In many real-world systems, we’re limited not by what we want to measure, but by what we can measure. Bandwidth, power, and time all constrain how much data a sensor can collect. Yet, remarkably, it’s often possible to reconstruct a complete signal from only a small fraction of the original data, provided that the signal is sparse in some domain.
This is where L1 minimization comes in. Sometimes called Basis Pursuit or Lasso Regression, L1 minimization is a mathematical technique used to recover sparse signals by finding the simplest solution that fits the available measurements. It underpins the theory of compressed sensing, which has transformed fields ranging from medical imaging and audio processing to low-power embedded sensing.
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