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Denoisers can help solve inverse problems via a recently proposed framework known as regularization by denoising (RED). The RED approach defines the regularization term of the inverse problem via explicit denoising engines. Simultaneous source separation techniques, being themselves a combination of inversion and denoising methods, provide a formidable field to explore RED. We investigate the applicability of RED to simultaneous-source data processing and introduce a deblending algorithm named REDeblending (RDB). The formulation permits developing deblending algorithms where the user can select any denoising engine that satisfies RED conditions. Two popular denoisers are tested, but the method is not limited to them: frequency-wavenumber thresholding and singular spectrum analysis. We offer numerical blended data examples to showcase the performance of RDB via numerical experiments.

Seismic data processing is a challenging task, especially when dealing with vector‐valued datasets. These data are characterized by correlated components, where different levels of uncorrelated random noise corrupt each one of the components. Mitigating such noise while preserving the signal of interest is a primary goal in the seismic‐processing workflow. The frequency‐space deconvolution is a well‐known linear prediction technique, which is commonly used for random noise suppression. This paper represents vector‐field seismic data through quaternion arrays and shows how to mitigate random noise by proposing the extension of the frequency‐space deconvolution to its hypercomplex version, the quaternion frequency‐space deconvolution. It also shows how a widely linear prediction model exploits the correlation between data components of improper signals. The widely linear scheme, named widely‐linear quaternion frequency‐space deconvolution, produces longer prediction filters, which have enhanced signal preservation capabilities shown through synthetic and field vector‐valued data examples.

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