  Electrocardiogram (EMG) signals play a significant role in decoding muscle
contraction information for robotic hand prosthesis controllers. Widely applied
decoders require large amount of EMG signals sensors, resulting in complicated
calculations and unsatisfactory predictions. By the biomechanical process of
single degree-of-freedom human hand movements, only several EMG signals are
essential for accurate predictions. Recently, a novel predictor of hand
movements adopts a multistage Sequential, Adaptive Functional Estimation (SAFE)
method based on historical Functional Linear Model (FLM) to select important
EMG signals and provide precise projections.
  However, SAFE repeatedly performs matrix-vector multiplications with a dense
representation matrix of the integral operator for the FLM, which is
computational expansive. Noting that with a properly chosen basis, the
representation of the integral operator concentrates on a few bands of the
basis, the goal of this study is to develop a fast Multiscale SAFE (MSAFE)
method aiming at reducing computational costs while preserving (or even
improving) the accuracy of the original SAFE method. Specifically, a multiscale
piecewise polynomial basis is adopted to discretize the integral operator for
the FLM, resulting in an approximately sparse representation matrix, and then
the matrix is truncated to a sparse one. This approach not only accelerates
computations but also improves robustness against noises. When applied to real
hand movement data, MSAFE saves 85%$\sim$90% computing time compared with SAFE,
while producing better sensor selection and comparable accuracy. In a
simulation study, MSAFE shows stronger stability in sensor selection and
prediction accuracy against correlated noise than SAFE.
