We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and measurement, and logarithmic in the ambient dimension where the signal is pres...

The effects of noise in the given phase o oignal reconstruction from the Fourier transform ohase are studied. Specifically, the effects of different methods of sampling the degraded phase, of the number of non—zero points in the sequence, and of the noise levol on the sequence reconstruction are examined. A sampling method is developef to significantly reduce the error in the reconstructed sequ...

The goal of this article is that of understanding how the oscillation and concentration effects developed by a sequence of functions in Rd are modified by the action of Sampling and Reconstruction operators on regular grids. Our analysis is performed in terms of Wigner and defect measures, which provide a quantitative description of the high frequency behavior of bounded sequences in L2 ( Rd ) ...

For reconstructing the signal from sampling data, the method based on Shannon’s Sampling theorem is usually employed. In this method, the reconstruction error appears when the signal does not satisfy the Nyquist condition. This paper proposes a new reconstruction method by using a linear perceptron and multi layer perceptron as FIR filter. The perceptron which has the weights obtained by learni...

Medical imaging is a useful technique for disease diagnosis and it has many applications in the medical field. There are several techniques used for medical imaging. Among them compression sensing (CS) technique has been widely accepted because of the low sample requirement and accurate recovery of image. In this paper, a novel adaptive matching pursuit for compressive sensing of blind sparsity...

analysis and enhancement which combines signal processing and symbolic processing in a closely coupled manner. The system takes as input both a noisy speech signal and a symbolic description of the speech signal. The system attempts to reconstruct the original speech waveform using symbolic processing to help model the signal and to guide reconstruction. The system uses various signal processin...

Multi-rate digital signal processing techniques have been developed in recent years for a wide range of applications, such as speech and image compression, statistical and adaptive signal processing and digital audio. Multi-rate statistical and adaptive signal processing methods provide solution to original signal reconstruction, using observation signals sampled at different rates. In this stu...

3 MTM-SVD Multivariate Frequency-Domain Climate Signal Detection and Reconstruction 32 3.1 Signal Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Signal Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3 Testing the Null hypothesis: Signi cance Estimation . . . . . . . . . 38 3.4 Application to Synthetic Dataset . . . . . . . . . . . . . . ....

Certain sparse signal reconstruction problems have been shown to have unique solutions when the signal is known to have an exact sparse representation. This result is extended to provide bounds on the reconstruction error when the signal has been corrupted by noise, or is not exactly sparse for some other reason. Uniqueness is found to be extremely unstable for a number of common dictionaries.