Unmasked and Masked Principles for Automatic Parameter Selection in Variational Models for Poisson Noise Corruption

  • Lanza, Alessandro (University of Bologna)
  • Bevilacqua, Francesca (University of Bologna)
  • Pragliola, Monica (University of Naples Federico II)
  • Sgallari, Fiorella (University of Bologna)

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Poisson noise is a pervasive cause of data degradation in many inverse imaging problems. Typical applications where Poisson noise removal is a crucial issue are astronomical and medical imaging. Both scenarios can in fact be characterized by a “low-light” condition, which is intrinsically related to the acquisition set-up in the former case, while in the latter it is somehow preferable so as to preserve the specimen of interest (microscopy) or keep the patient safer by irradiating lower electromagnetic doses (CT). However, the weaker the light intensity, the stronger the Poisson noise degradation in the acquired images and the more difficult the reconstruction problem. Variational methods are an effective model-based approach for reconstructing images corrupted by Poisson noise. However, their performance strongly depends on a suitable selection of the regularization parameter balancing the effect of the regulation term(s) and the data fidelity term. One of the approaches still most used today for choosing the parameter is the discrepancy principle proposed in [1]. It relies on imposing a value of the data term approximately equal to its expected value and works quite well for mid- and high-photon counting scenarios. However, the approximation used in the theoretical derivation of the expected value leads to poor performance for low-count Poisson noise. The talk will illustrate three novel parameter selection strategies which are demonstrated to outperform the state-of-the-art discrepancy principle in [1], especially in the low-count regime. The three approaches rely on decreasing the approximation error in [1] by means of a suitable Montecarlo simulation [2], on applying a so-called Poisson whiteness principle [3] and on cleverly masking the data used for the parameter selection [4], respectively. Extensive experiments are presented which prove the effectiveness of the three novel methods.