Distributed compressed sensing theory is applied to many practical problems, ECG signal, color imaging, etc. In order to improve the reconstruction accuracy of multi-dimensional signals, this paper applies singular value decomposition to the multi-measure vector problem in DCS, then distributed compressed sensing reconstruction method based on singular value decomposition is proposed. This method can achieve row orthogonality of the measurement matrix and does not affect the design of the reconstruction matrix. Numerical experiments verify the effectiveness of the proposed method, which can significantly improve the reconstruction quality of the signal and the robustness to noise.
Compressed ghost imaging can effectively enhance the quality of original image from far fewer measurements, but due to the non-negativity of the measurement matrix, the recover quality is thus limited. In this paper, singular value decomposition compressed ghost imaging is proposed; First, the singular value decomposition be used to decompose the measurement matrix, and then the optimized measurement matrix and measurements are used to recover the original image. Numerical experiments verify the superiority of our proposed singular value decomposition compression ghost imaging method.
Reconstruction of the lost phase information in the complex optical field from a single-intensity measurement in the Fourier domain is often termed as phase retrieval. This method can be used in many fields, such as electron microscopy, wavefront sensing, astronomy and crystallography and so on. The classical phase retrieval methods use the two-intensity measurements recorded or single-intensity measurement recorded with some prior knowledge, which utilizes the Gerchberg-Saxton(GS)-like algorithm to iteratively recover the phase of the complex optical field. Aiming at the problem that the single-intensity phase retrieval method has poor reconstruction quality and low probability of successful recovery in practical application, an improved method is proposed in this paper—two-step phase retrieval algorithm from single-exposure measurement. Our proposed method divides the phase retrieval into two steps: first, the GS algorithm combined with prior knowledge is used to recover the amplitude information in the spatial domain from the single-spread Fourier spectrum, and then the classical GS algorithm using two-intensity measurements (one is recorded and the other is estimated from the first step) is used to recover the phase information of the complex optical field behind the coded aperture. Finally, the effectiveness of the proposed method is verified by numerical experiments. Compared with the single-intensity phase retrieval method, our proposed method can significantly improve the reconstruction quality and probability of successful recovery.
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