  For an ill-posed inverse problem, particularly with incomplete and limited
measurement data, regularization is an essential tool for stabilizing the
inverse problem. Among various forms of regularization, the lp penalty term
provides a suite of regularization of various characteristics depending on the
value of p. When there are no explicit features to determine p, a spatially
varying inhomogeneous p can be incorporated to apply different regularization
characteristics that change over the domain. This study proposes a strategy to
design the exponent p when the first and second derivatives of the true signal
are not available, such as in the case of indirect and limited measurement
data. The proposed method extracts statistical and patch-wise information using
multiple reconstructions from a single measurement, which assists in
classifying each patch to predefined features with corresponding p values. We
validate the robustness and effectiveness of the proposed approach through a
suite of numerical tests in 1D and 2D, including a sea ice image recovery from
partial Fourier measurement data. Numerical tests show that the exponent
distribution is insensitive to the choice of multiple reconstructions.
