  Recently, multidimensional signal reconstruction using a low number of
measurements is of great interest. Therefore, an effective sampling scheme
which should acquire the most information of signal using a low number of
measurements is required. In this paper, we study a novel cube-based method for
sampling and reconstruction of multidimensional signals. First, inspired by the
block-based compressive sensing (BCS), we divide a group of pictures (GoP) in a
video sequence into cubes. By this way, we can easily store the measurement
matrix and also easily can generate the sparsifying basis. The reconstruction
process also can be done in parallel. Second, along with the Kronecker
structure of the sampling matrix, we design a weight matrix based on the human
visuality system, i.e. perceptually. We will also benefit from different
weighted $\ell_1$-minimization methods for reconstruction. Furthermore,
conventional methods for BCS consider an equal number of samples for all
blocks. However, the sparsity order of blocks in natural images could be
different and, therefore, a various number of samples could be required for
their reconstruction. Motivated by this point, we will adaptively allocate the
samples for each cube in a video sequence. Our aim is to show that our simple
linear sampling approach can be competitive with the other state-of-the-art
methods.
