The Design Of Ridgelet Redundant Dictionaries And Reconstruction Algorithm

With the increasing of information that people demand, image compressing methods based on traditional sampling technology lead to a large amount of storage and transmission costs. Meanwhile, traditional sampling technology requires a higher sampling rate of hardware devices. In order to solve the bottleneck problem caused by traditional sampling, compressed sensing theory has brought a revolutionary breakthrough for data collection technology. In the compressed sensing theory sampling rate is well below the Nyquist frequency, using non-adaptive linear projection to maintain the original structure of the signal, and reconstructing the original signal accurately by solving optimization problem. At present the theoretical study of compressed sensing has attracted a growing number of researcher’s attention.Compressed sensing theory mainly involves three aspects, which are signal sparse express, observation matrix design and signal reconstruction. So we need to solve three problems, i.e. how to find the original sparse domain, how to design sparse measurement matrix which is not related to sparse domain, and to find a fast reconstruction algorithm which can reconstruct original signal accurately. This paper focuses on sparse representation and signal reconstruction.To the former, for the hot issues in sparse representation field which is signal sparse in the redundant dictionary, beginning from the problem that how to construct a certain type redundant dictionary, we design a redundant dictionary which is based on the framework of ridgelet, according to the texture characteristics of the image and the line singularity characteristics of ridgelet. Considering that the scale of the redundant dictionary which is used to high-dimensional image sparse representation is too large, in the processing of designing dictionary, we adopt blocking idea, which reduce the time complexity greatly. The simulation results show that our dictionary makes better sparse representation results comparing with other redundant dictionaries.For the latter, there are lots of reconstruction algorithms already, for example OMP and BP. Although there are a growing number of scholars making their eyes to the field of compressed sensing, the using of redundant dictionary in compressed sensing is still rare. In this article we have made a try on this. We apply the redundant dictionary which is constructed by us to compressed sensing and design one kind of reconstruction algorithm which is based on the idea of biological evolution, which get the approximate global optimal solution by evolutionary searching. In this article, the simulation experiments show that our algorithm make more better reconstruction results, but the time complexity need to be improved in the future.