Shearlet regularization and dimensionality reduction for the temperature distribution sensing

• A dimensionality reduction based method is proposed to model the TDS problem.
• The PNMF method is developed to extract the basis vectors from a set of snapshots.
• An objective functional is proposed to cast the TDS task as a minimization problem.
• An iteration scheme is developed to solve the proposed objective functional.
• The feasibility of the proposed method is numerically validated.

In this paper, a new dimensionality reduction based temperature distribution sensing (TDS) method is proposed to reconstruct the temperature distribution via the limited number of the scattered temperature measurement data. The projective nonnegative matrix factorization (PNMF) method is developed to exact the basis vectors, and the augmented Lagrangian multipliers (ALM) method is proposed to solve the proposed PNMF model. A dimensionality reduction model is obtained via projecting the original temperature distribution onto the spaces spanned by a set of basis. An objective functional that considers the inaccurate properties of the reconstruction model and the measurement data, the Shearlet regularization and the total variation (TV) method is proposed to convert the TDS task into an optimization problem, where the temperature distribution is indirectly reconstructed via solving a low-dimensional vector. An iteration scheme is developed to solve the objective functional. Numerical simulation results validate the feasibility of the proposed reconstruction algorithm.