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. Author manuscript; available in PMC: 2013 Dec 12.

Published in final edited form as: IEEE Trans Signal Process. 2011 Jun 20;59(10):10.1109/TSP.2011.2160058. doi: 10.1109/TSP.2011.2160058

Fig. 1 — Illustration of the three approximations of the manifold of translates of the waveform, (a) The standard basis pursuit (BP) dictionary, F_Δ, as used in Eq. (7), consists of discrete time-shifts of the waveform f(t). (b) Continuous basis pursuit with first-order Taylor interpolator (CBP-T), as specified by Eq. (13). Each pair of functions, (f_i_Δ, $f_{i Δ}^{'}$ ), with properly constrained coefficients, represents a triangular region of the space (shaded regions). (c) Continuous basis pursuit with polar interpolation (CBP-P), as specified by Eq. (20). Each triplet of functions, (c_i_Δ, u_i_Δ, v_i_Δ), represents a section of a cone (see Fig. 3(b) for parameterization).

Inline graphic — Illustration of the three approximations of the manifold of translates of the waveform, (a) The standard basis pursuit (BP) dictionary, F_Δ, as used in Eq. (7), consists of discrete time-shifts of the waveform f(t). (b) Continuous basis pursuit with first-order Taylor interpolator (CBP-T), as specified by Eq. (13). Each pair of functions, (f_i_Δ, $f_{i Δ}^{'}$ ), with properly constrained coefficients, represents a triangular region of the space (shaded regions). (c) Continuous basis pursuit with polar interpolation (CBP-P), as specified by Eq. (20). Each triplet of functions, (c_i_Δ, u_i_Δ, v_i_Δ), represents a section of a cone (see Fig. 3(b) for parameterization).