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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 47255 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Amini, Arash
- Abstract:
- Compressed sensing theory with the goal of sparse recovery using as few measurements as possible, has found much attention in the past decade. A fundamental assumption in compresses sensing is the linear nature of the measurements, that establishes a matrix equation between the unknowns and unknowns. However, in some applications, the physics of the problem may impose some type of nonlinear relationship between the unknowns and the measurements. Some solutions concerned with this type of problems,approximate the nonlinear relationship using a second order Taylor expansion. Using this approximation besides some modifications in the way the second order relationship is presented, a more simple framework is obtained. Although, the current algorithms and methods are not strong enough to solve the problem defined in this framework with anacceptable quality. Regarding this fact, one can conclude that nonlinearity is undesirable from the view of this solution and it has to be avoided in any way. In this thesis, we have shown that this is not generally true. Conversely, in some cases nonlinearity can bring us some advantages. To make this more specific, we have introduced a nonlinear sampling and reconstruction technique which is able to recover a k -sparse vector using as few measurements as 2k . This number is referred to as the least achievable rate in many references. The mentioned method is sensitive to noise, which limits its usage to a few applications. We have also introduced a linear recovery method which is fundamentally similar to the mentioned nonlinear technique. This method may compete with usual convex optimization techniques in compressed sensing in terms of speed and quality of recovery. The mentioned method is not first offered by us and our main contribution in this work is the proposition of two modifications which highly improves the recovery quality. An interesting point about the two mentioned techniques is that one can suggest a new technique with the combination of these methods. The new technique samples the signal nonlinearly, but reconstructs it linearly as in these two techniques. Simulation results confirm that the proposed method is much less sensitive to noise comparing to the primary nonlinear technique
- Keywords:
- Compressive Sensing ; Nonlinear Sampling ; Nonlinear Recovery ; Active Coefficients ; Annihilating Filter
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