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Compressive sampling and simulation of one-pixel camera
Hrbáček, Radek ; Špiřík, Jan (referee) ; Rajmic, Pavel (advisor)
The Nyquist theorem is the main pillar of the traditional digital signal processing approach. It states that the sampling rate must be at least twice the maximum frequency present in the signal to guarantee perfect signal reconstruction from the sequence of its samples. In practice, we often compress the signal right after the sampling process to reduce the data size. The compressive sampling approach is not limited to the frequency domain, it provides a new look at the signal by using an arbitrary basis. If we find a basis in which the signal is sparse, it is possible to take a small number of samples and reconstruct the signal successfully. One-pixel camera is one of real applications, it's formed by digital micromirror array reflexing the light into single sensor. Mathematical methods are then used to reconstruct the signal. This thesis deals with the simulation of the camera.
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Restoration of signals with limited instantaneous value using a psychoacoustic model
Beňo, Tomáš ; Rajmic, Pavel (referee) ; Záviška, Pavel (advisor)
The master's thesis deals with the restoration of audio signals that have been damaged by clipping. Used methods are based on sparse representations of signals. The introduction of the thesis explains the issue of clipping and mentions the list of already existing methods that solve declipping, which are followed by the thesis. In the next chapter, the necessary theory of sparse representations and the proximal algorithms is described, including specific representatives from the category of convex optimization problems. The thesis contains declipping algorithm implemented in Matlab software environment. Chosen method for solving the task uses the Condat algorithm or Generic proximal algorithm for convex optimization and solves minimization of sum of three convex functions. The result of the thesis is five versions of algorithm and three of them have implemented psychoacoustic model for results improvement. For each version has been found optimal setting of parameters. The restoration quality results are evaluated using objective measurements like SDR and PEMO-Q and also using subjective listening test.
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Restoration of signals with limited instantaneous value using a psychoacoustic model
Beňo, Tomáš ; Rajmic, Pavel (referee) ; Záviška, Pavel (advisor)
The master's thesis deals with the restoration of audio signals that have been damaged by clipping. Used methods are based on sparse representations of signals. The introduction of the thesis explains the issue of clipping and mentions the list of already existing methods that solve declipping, which are followed by the thesis. In the next chapter, the necessary theory of sparse representations and the proximal algorithms is described, including specific representatives from the category of convex optimization problems. The thesis contains declipping algorithm implemented in Matlab software environment. Chosen method for solving the task uses the Condat algorithm or Generic proximal algorithm for convex optimization and solves minimization of sum of three convex functions. The result of the thesis is five versions of algorithm and three of them have implemented psychoacoustic model for results improvement. For each version has been found optimal setting of parameters. The restoration quality results are evaluated using objective measurements like SDR and PEMO-Q and also using subjective listening test.
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Compressive sampling and simulation of one-pixel camera
Hrbáček, Radek ; Špiřík, Jan (referee) ; Rajmic, Pavel (advisor)
The Nyquist theorem is the main pillar of the traditional digital signal processing approach. It states that the sampling rate must be at least twice the maximum frequency present in the signal to guarantee perfect signal reconstruction from the sequence of its samples. In practice, we often compress the signal right after the sampling process to reduce the data size. The compressive sampling approach is not limited to the frequency domain, it provides a new look at the signal by using an arbitrary basis. If we find a basis in which the signal is sparse, it is possible to take a small number of samples and reconstruct the signal successfully. One-pixel camera is one of real applications, it's formed by digital micromirror array reflexing the light into single sensor. Mathematical methods are then used to reconstruct the signal. This thesis deals with the simulation of the camera.
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