Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
Block sparsity and sampling over a union of subspaces
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Multirate synchronous sampling of sparse multiband signals
IEEE Transactions on Signal Processing
Time-delay estimation from low-rate samples: a union of subspaces approach
IEEE Transactions on Signal Processing
Learning with Structured Sparsity
The Journal of Machine Learning Research
Recovery of the optimal approximation from samples in wavelet subspace
Digital Signal Processing
On MAP and MMSE estimators for the co-sparse analysis model
Digital Signal Processing
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One of the fundamental assumptions in traditional sampling theorems is that the signals to be sampled come from a single vector space (e.g., bandlimited functions). However, in many cases of practical interest the sampled signals actually live in a union of subspaces. Examples include piecewise polynomials, sparse representations, nonuniform splines, signals with unknown spectral support, overlapping echoes with unknown delay and amplitude, and so on. For these signals, traditional sampling schemes based on the single subspace assumption can be either inapplicable or highly inefficient. In this paper, we study a general sampling framework where sampled signals come from a known union of subspaces and the sampling operator is linear. Geometrically, the sampling operator can be viewed as projecting sampled signals into a lower dimensional space, while still preserving all the information. We derive necessary and sufficient conditions for invertible and stable sampling operators in this framework and show that these conditions are applicable in many cases. Furthermore, we find the minimum sampling requirements for several classes of signals, which indicates the power of the framework. The results in this paper can serve as a guideline for designing new algorithms for various applications in signal processing and inverse problems.