چكيده به لاتين
Abstract:
Compressive sensing is a new pattern in the field of signal processing which mixes sampling and compressing of sparse signals using a linear measurement procedure less than Nyquist rate so that the result is an output vector consisting of a few number of measurements and afterward, using a proper recovery algorithm the most sparsest signal is recovered which matches the measurements.
Compressive sensing on a graph; signals could be estimated by graphs and nodes containing information. There are tow reasons why compressive sensing on graphs is important: because of intense cost of one-by-one checking of parameters and direct inaccessibility to information of some of the parameters in the graph. Structural limitations of graphs cause some differences between conventional and compressive sensing which distinguish them. One of the most important of these differences is the construction of measurement matrix. In order to construct the measurement matrix in conventional sensing, random Gaussian matrix is used. But because all of the observation on the graph we have had are non-negative coefficients, this matrix can’t be used to construct measurement matrix in the field of graph. One of the ways to construct this matrix in the field of graph is the Random Walk although because of the construction and limitations of the network, any observation on the graph is not possible and this problem can lead to weak recovery of initial vector. Family of measurement matrixes which could be applied in compressive sensing on graph, are more limited than matrixes in the field of conventional sensing (video or sound) and need to be proportional to the graph’s (network) construction.
Active learning, is a subset of machine vision and generally artificial intelligence. The key idea is that if the learning algorithm is allowed to choose the information that should be learned by itself, then the algorithm will have better performance with less learnings.
In the current work, using the idea of active learning, we’ve tried to introduce a method to improve the construction of measurement matrix in the field of graph to recognize the probably missed information of the graph in construction of measurement matrix (assuming that measurement matrix is sub-determined and non-adaptive), by random walk method and after observation, insert those information in the measurement matrix to have a stronger recovery of the initial graph.
In order to evaluate this method, first using five hundred nodes as initial signal, the measurement matrix is constructed by two methods: random walk and our suggested method, and using that we achieve the output vector. Then, the initial sparse signal is reviewed by two algorithms: the convex optimization recovery algorithm and Ising model, and finally calculate the amount of error and amount of similarity of four recovered signal to initial signal and by comparing them we get to know that recovery of sparse signal from the constructed matrix based on our suggested method and based on convex optimization recovery algorithm, has the most amount of similarity and the least amount of error to initial signal, compared to other three recovered signal.
Keywords: Compressive sensing, constructional limitation of graph, measurement matrix, active learning.
