2016/01/08 by Chen Li, Ben Adcock, Li, Chen +1
Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1601.01988
openalex publication_date 2016/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has recently found applications in problems such as compressive imaging, multi-sensor acquisition systems and sparse regularization in inverse problems. In this paper we present uniform recovery guarantees for this class when the measurement matrix corresponds to a subsampled isometry. We do this by establishing a variant of the standard restricted isometry property for sparse in levels vectors, known as the restricted isometry property in levels. Interestingly, besides the usual log factors, our uniform recovery guarantees are simpler and less stringent than existing nonuniform recovery guarantees. For the particular case of discrete Fourier sampling with Haar wavelet sparsity, a corollary of our main theorem yields a new recovery guarantee which improves over the current state-of-the-art.