Practical error estimates for sparse recovery in linear inverse problems
For practitioners using sparse recovery in inverse problems, this work offers practical error bounds that account for realistic conditions, though the contribution is incremental.
The paper studies the reconstruction quality of sparse recovery methods in linear inverse problems under non-idealized conditions, providing practical error estimates that depend on sparsity, data quantity, noise level, and measurement matrix properties, validated on a magnetic tomography example.
The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors (depending on the sparsity of the desired solution, the number of data, the noise level on the data, and various properties of the measurement matrix); they are compared to known theoretical bounds and illustrated on a magnetic tomography example.