Final Report Summary - SPARSAM (Sparse Sampling: Theory, Algorithms and Applications)
Signal representations with Fourier and wavelet bases are central to signal processing and communications. Non-linear approximation methods in such bases are key for problems like denoising, compression and inverse problems. Recently, the idea that signals that are sparse in some domain can be acquired at low sampling density has generated strong interest, under various names like compressed sensing, compressive sampling and sparse sampling.
In this project, we have studied the central problem of acquiring continuous-time signals for discrete-time processing and reconstruction using the methods of sparse sampling. Solving this involved theoretical developments and new algorithms for sparse sampling, both in continuous and discrete time. In addition, in order to acquire physical signals, we developed a sampling theory for signals obeying physical laws, like the wave and diffusion equation, and light fields.
We have thus developed a sparse sampling theory and framework for signal processing and communications, with applications ranging from analog-to-digital conversion to new compression methods, to super-resolution data acquisition and to inverse problems. In particular, we used time-of-flight measurements to solve the open inverse problem ‘’can one hear the shape of a room?’' which has applications in indoor localization.
In sum, we developed the theory and associated algorithms for sparse signal processing, with impact on a broad range of applications.
In this project, we have studied the central problem of acquiring continuous-time signals for discrete-time processing and reconstruction using the methods of sparse sampling. Solving this involved theoretical developments and new algorithms for sparse sampling, both in continuous and discrete time. In addition, in order to acquire physical signals, we developed a sampling theory for signals obeying physical laws, like the wave and diffusion equation, and light fields.
We have thus developed a sparse sampling theory and framework for signal processing and communications, with applications ranging from analog-to-digital conversion to new compression methods, to super-resolution data acquisition and to inverse problems. In particular, we used time-of-flight measurements to solve the open inverse problem ‘’can one hear the shape of a room?’' which has applications in indoor localization.
In sum, we developed the theory and associated algorithms for sparse signal processing, with impact on a broad range of applications.