Many atmospheric measurement techniques involve inversion of photon counts detected by multi-spectral sensors spanning the X-ray to microwave regions of the electromagnetic spectrum. Although photon counts follow Poisson statistics, commonly used inversion techniques often rely on statistical assumptions that disregard the Poisson nature of the sensor data, limiting the scientific utility of datasets. Motivated to overcome this limiting assumption, this study focuses on retrieval techniques that involve the ratio of counts received in different sub-bands and introduces a new computationally efficient and robust approach to this type of inverse problem that respects the underlying count statistics. The method assumes that the received photon counts in each channel are a realization of a binned point process, allowing the ratio of the channel intensities to be modeled within a hierarchical Bayesian framework. This allows us to directly incorporate correlation between the bins via the prior that is modeled using a permanental process. It further enables more accurate uncertainty quantification without costly sampling procedures common in Bayesian inversion methods. The method is verified and validated on thermospheric neutral temperature retrievals from simulated top-of-atmosphere far-ultraviolet (FUV) disk emission data corresponding to 2<span>–</span>8 November 2018, which includes a minor geomagnetic storm. It is also demonstrated on calibrated photon counts data from the NASA Global-scale Observations of the Limb and Disk (GOLD) mission from the same time period and from 11 May 2024 during a severe geomagnetic storm. The study demonstrates the method's ability to accurately recover neutral temperature in a variety of geomagnetic conditions, attesting to its potential to extend the fidelity of neutral temperature retrievals over broader solar zenith angles than currently possible with existing techniques.