  Recently, many convolutional neural network (CNN) methods have been designed
for hyperspectral image (HSI) classification since CNNs are able to produce
good representations of data, which greatly benefits from a huge number of
parameters. However, solving such a high-dimensional optimization problem often
requires a large amount of training samples in order to avoid overfitting.
Additionally, it is a typical non-convex problem affected by many local minima
and flat regions. To address these problems, in this paper, we introduce naive
Gabor Networks or Gabor-Nets which, for the first time in the literature,
design and learn CNN kernels strictly in the form of Gabor filters, aiming to
reduce the number of involved parameters and constrain the solution space, and
hence improve the performances of CNNs. Specifically, we develop an innovative
phase-induced Gabor kernel, which is trickily designed to perform the Gabor
feature learning via a linear combination of local low-frequency and
high-frequency components of data controlled by the kernel phase. With the
phase-induced Gabor kernel, the proposed Gabor-Nets gains the ability to
automatically adapt to the local harmonic characteristics of the HSI data and
thus yields more representative harmonic features. Also, this kernel can
fulfill the traditional complex-valued Gabor filtering in a real-valued manner,
hence making Gabor-Nets easily perform in a usual CNN thread. We evaluated our
newly developed Gabor-Nets on three well-known HSIs, suggesting that our
proposed Gabor-Nets can significantly improve the performance of CNNs,
particularly with a small training set.
