  Component separation for the Planck HFI data is primarily concerned with the
estimation of thermal dust emission, which requires the separation of thermal
dust from the cosmic infrared background (CIB). For that purpose, current
estimation methods rely on filtering techniques to decouple thermal dust
emission from CIB anisotropies, which tend to yield a smooth, low- resolution,
estimation of the dust emission. In this paper we present a new parameter
estimation method, premise: Parameter Recovery Exploiting Model Informed Sparse
Estimates. This method exploits the sparse nature of thermal dust emission to
calculate all-sky maps of thermal dust temperature, spectral index and optical
depth at 353 GHz. premise is evaluated and validated on full-sky simulated
data. We find the percentage difference between the premise results and the
true values to be 2.8, 5.7 and 7.2 per cent at the 1{\sigma} level across the
full sky for thermal dust temperature, spectral index and optical depth at 353
GHz, respectively. Comparison between premise and a GNILC-like method over
selected regions of our sky simulation reveals that both methods perform
comparably within high signal-to-noise regions. However outside of the Galactic
plane premise is seen to outperform the GNILC-like method with increasing
success as the signal-to-noise ratio worsens.
