Atomic Decomposition of Mixtures of Translation-Invariant Signals
نویسندگان
چکیده
This paper develops a theory for the atomic decomposition of mixtures of translation-invariant signals. Suppose we have a linear combination of shifted copies of a known waveform with unknown shifts and coefficients. These shifts assume continuous values on the real line. We show that one can recover the exact translations and amplitudes by solving a continuous analog of `1 minimization, provided the translations are well separated. The minimal separation depends on properties of the auto-correlation function of the known waveform. This work lays a foundation for the study of denoising and reconstruction of translation-invariant signals from linear measurements, and finds applications in microscopy imaging, radar, and communication.
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