Sparhorisonten

Sparhorisonten is a concept used in information theory and signal processing to describe a boundary beyond which the recovery of sparse signals from compressed measurements becomes unreliable. It captures the practical limit of reconstruction under sparsity constraints.

Etymology: The term combines spar, referring to sparsity, with horisont, meaning horizon, and is used primarily in Nordic discussions of compressed sensing and related fields.

Concept: In a d-dimensional signal that is k-sparse (only k nonzero components), reconstruction from m linear measurements is possible under standard assumptions when m exceeds a threshold that depends on k and d. The sparhorisonten is the practical boundary: below it, many distinct k-sparse signals can produce indistinguishable measurements, while above it, stable or exact recovery is achievable with high probability given suitable measurement matrices (for example, satisfying restricted isometry properties). In practice, the horizon depends on factors such as noise, model mismatch, and recovery algorithm.

Applications and implications: The concept informs the design of sensors, imaging systems, wireless communications, and data compression by indicating how many measurements or sensing elements are needed to reliably recover sparse signals.

See also: sparsity, compressed sensing, restricted isometry property, sparse recovery.