LS-CS-residual (LS-CS): Compressive Sensing on Least Squares Residual
arXiv:0911.5524 · doi:10.1109/TSP.2010.2048105
Abstract
We consider the problem of recursively and causally reconstructing time sequences of sparse signals (with unknown and time-varying sparsity patterns) from a limited number of noisy linear measurements. The sparsity pattern is assumed to change slowly with time. The idea of our proposed solution, LS-CS-residual (LS-CS), is to replace compressed sensing (CS) on the observation by CS on the least squares (LS) residual computed using the previous estimate of the support. We bound CS-residual error and show that when the number of available measurements is small, the bound is much smaller than that on CS error if the sparsity pattern changes slowly enough. We also obtain conditions for "stability" of LS-CS over time for a signal model that allows support additions and removals, and that allows coefficients to gradually increase (decrease) until they reach a constant value (become zero). By "stability", we mean that the number of misses and extras in the support estimate remain bounded by time-invariant values (in turn implying a time-invariant bound on LS-CS error). The concept is meaningful only if the bounds are small compared to the support size. Numerical experiments backing our claims are shown.
Accepted (with mandatory minor revisions) to IEEE Trans. Signal Processing. 12 pages, 5 figures
References in corpus (3)
Cited by in corpus (26)
- Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
- Distributed Compressive Sensing: A Deep Learning Approach
- Recursive Recovery of Sparse Signal Sequences from Compressive Measurements: A Review
- Regularized Modified BPDN for Noisy Sparse Reconstruction with Partial Erroneous Support and Signal Value Knowledge
- Dynamic Filtering of Time-Varying Sparse Signals via l1 Minimization
- Adaptive-Rate Compressive Sensing Using Side Information
- ReProCS: A Missing Link between Recursive Robust PCA and Recursive Sparse Recovery in Large but Correlated Noise
- Sparse Bayesian Learning with Dynamic Filtering for Inference of Time-Varying Sparse Signals
- Dynamic Iterative Pursuit
- Exploiting Correlation in Sparse Signal Recovery Problems: Multiple Measurement Vectors, Block Sparsity, and Time-Varying Sparsity
- KF-CS: Compressive Sensing on Kalman Filtered Residual
- Real-time Dynamic MRI Reconstruction using Stacked Denoising Autoencoder
- Exact Reconstruction Conditions for Regularized Modified Basis Pursuit
- Widely Distributed Radar Imaging: Unmediated ADMM Based Approach
- Stability (over time) of Modified-CS and LS-CS for Recursive Causal Sparse Reconstruction
- Parallel Unbalanced Optimal Transport Regularization for Large Scale Imaging Problems
- PaFiMoCS: Particle Filtered Modified-CS and Applications in Visual Tracking across Illumination Change
- Tracking Tensor Subspaces with Informative Random Sampling for Real-Time MR Imaging
- A Unified Algorithmic Framework for Dynamic Compressive Sensing
- Efficient Estimation of Compressible State-Space Models with Application to Calcium Signal Deconvolution
- Time Invariant Error Bounds for Modified-CS based Sparse Signal Sequence Recovery
- Probabilistic Recovery Guarantees for Sparsely Corrupted Signals
- Prior Support Knowledge-Aided Sparse Bayesian Learning with Partly Erroneous Support Information
- Stability of Modified-CS and LS-CS for Recursive Reconstruction of Sparse Signal Sequences
- Dynamic Sample Complexity for Exact Sparse Recovery using Sequential Iterative Hard Thresholding
- RL-NCS: Reinforcement learning based data-driven approach for nonuniform compressed sensing