Maryia Kabanava

STABLE LOW-RANK MATRIX RECOVERY VIA NULL SPACE PROPERTIES

The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modeled probabilistically. We derive sufficient conditions on the minimal amount of measurements ensuring recovery via convex optimization. We establish our results via certain properties of the null space of the measurement map. In the setting where the measurements are realized as Frobenius inner products with independent standard Gaussian random matrices we show that

Robust analysis ℓ1-recovery from Gaussian measurements and total variation minimization

10 r (n_1 + n_2)

Cosparsity in Compressed Sensing

measurements are enough to uniformly and stably recover an

Analysis of low rank matrix recovery via Mendelson's small ball method

n_1 \times n_2

On the minimal number of measurements in low-rank matrix recovery

matrix of rank at most

Characterization of Besov Spaces on Nested Fractals by Piecewise Harmonic Functions

r

Function spaces on the Koch curve

. We then significantly generalize this result by only requiring independent mean-zero, variance one entries with four finite moments at the cost of replacing

Analysis ℓ1-recovery with Frames and Gaussian Measurements

10

Tempered Radon Measures

by some universal constant. We also study the case of recovering Hermitian rank-

Besov spaces on fractals and tempered Radon measures

r