The Research Of Frame Theory For Signal Coding Erasure

In the signa l transmission and restoration process, the error is inevitable by the missing data and quantization noise. The fram e-based coding is used to solving this problem. Redundancy is an interesting and attractive feature of frames, because it has at least two a dvantages. First, it m akes the co nstruction of various classes of fram es flexible; secondly, it can enhance the robustness of data when erasures occur in signal transmissions. According to this property, this paper studies the selecting of the optimal dual frame which contains the quantization noi se. For the a pplication of fusion frames in the experimental data transmission, we construct the dual fusion frame system with its local dual frames.For the data loss problems during the transmission of signal, we can reconstruct the signal using of the redundancy of fra me. If the signal can not be com pletely reconstructed, we select the appropriate framework to minimize the reconstruction error. In this paper, we investigate the optimal dual frames which minimize the reconstruction error based on a new error m odel involving th e quantization noise for the data loss problems in the signal transm ission process, and obtain the necessary and sufficient condition under which the canonical dual fram e is the unique optim al dual for k-erasures. When the coding fr ame is tight, we explore so me sufficient conditions to judge whether the canonical dual fram e is the optimal dual fram e for 1-erasure. For practical application, When we don’t know which data is lost for 1-erasure, we find the average of the mean square error（_<sub><sub><sub><sub><sub>1MSE） a substitute for the mean square error（1MSE）. When the coding frame is uniform tight, we explore some sufficient conditions to judge whether the canonical dual fram e is not the optimal dual frame for 1-erasure. F inally, we give an example which sho ws that th e optimal dual frame is di fferent from the ”optimal duals” which ignores the quantization noise, and we compare the im age restoration effects.The experimental data transm ission is an important part of high energy physics experiment. The utilization of fusion fra mes for data transm ission coding can enhance the transmission efficiency. For this applica tion, we research the class of fusion fra mes in a Hilbert space. By using the m atrix representation of the fusion frame operato r of a given fusion fra me system, we provide an algorithm for constructing the dual fusionframe system with its local dual frames which can be used as data transmission coder in the high energy physics experim ents. Finally, we present a simulation example of data coding to show the practicability and validity of our results.