Short Note Sparse radon transforms with a bound-constrained approach

Radon transforms are popular operators for velocity analysis (Taner and Koehler, 1969; Guitton and Symes, 2003), noise attenuation (Foster and Mosher, 1992), and data interpolation (Hindriks and Duijndam, 1998; Trad et al., 2002). One property that is often sought in radon domains is sparseness, where the energy in the model space is well focused for each corresponding event in the data space. Sparseness is especially useful for multiple attenuation and interpolation. In practice, depending on the radon transform, sparseness can be achieved either in the Fourier (Herrmann et al., 2000) or time domain (Sacchi and Ulrych, 1995). To estimate sparse radon panels in the time domain, a regularization operator that enforces longtailed probability density functions for the model parameters is often used. This regularization operator can be the `1 norm (Nichols, 1994) or the Cauchy norm (Sacchi and Ulrych, 1995).