Using Data Imputation for Signal Separation in High-contrast Imaging

Abstract

To characterize circumstellar systems in high-contrast imaging, the fundamental step is to construct a best point-spread function (PSF) template for the noncircumstellar signals (i.e., starlight and speckles) and separate it from the observation. With existing PSF construction methods, the circumstellar signals (e.g., planets, circumstellar disks) are unavoidably altered by overfitting and/or self-subtraction, making forward modeling a necessity to recover these signals. We present a forward modeling–free solution to these problems with data imputation using sequential nonnegative matrix factorization (DI-sNMF), which first converts this signal separation problem to a "missing data" problem in statistics by flagging the regions that host circumstellar signals as missing data, then attributes PSF signals to these regions. We mathematically prove it to have negligible alteration to circumstellar signals when the imputation region is relatively small, which thus enables precise measurement of these circumstellar objects. We apply it to simulated point-source and circumstellar disk observations to demonstrate its proper recovery of them. We apply it to Gemini Planet Imager K1-band observations of the debris disk surrounding HR 4796A, finding a tentative trend that the dust is more forward scattering as the wavelength increases. We expect DI-sNMF to be applicable to other general scenarios where the separation of signals is needed.

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