A Simple Way to Discrete Signal Reconstruction

What is it about?

This paper gives a simple way to reconstruct discrete signals, e.g. binary-valued signals, from incomplete linear measurements based on sum-of-absolute-values optimisation. Also, the paper shows a relationship between discreteness and sparsity.

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Why is it important?

Discrete signal reconstruction is important in binary (or low-bit) image processing, symbol detection in wireless communications, discrete-valued control such as PWM (pulse width modulation) control, etc. Conventionally, such a problem is described in integer-valued optimisation, which is quite hard to solve when the problem is large. Alternatively, the paper proposes to reduce the problem to sum-of-absolute-values optimisation, which is convex and hence easy to solve.