چكيده به لاتين
We study blind deconvolution based on the sparsity of the input signal in the value domain. Blind deconvolution is an inverse bilinear problem which discusses recovering signal and kernel simultaneously, in other words recovering two vectors from their linear or circular convolution. Various applications such as Image De-blurring, Seismic data analysis, and Channel equalization can be described in this framework. without considering special assumptions, blind deconvolution has too many solutions and cannot lead to unique answer. Until now, some limitations has been assumed which help to recover the unique solutions in such problems. These assumptions contain subspace, sparsity and combined limitations. Most of these assumptions which has been made till now, are not correct practically. In the thesis, we assume that the input signal of the channel has a modulation so that the values which are passing through the communication channel belong to a Collection with finite values. we introduce a method to estimate both unknowns, signal and channel response, without common assumptions which other previous papers have assumed. we first introduce a transformation function which can transform the input signal of the channel to a sparse vector and then solve the problem as a convex optimization in the form of a positive semi-definite problem minimizing the l_1 norm.
