Exploiting sparsity in the image gradient magnitude has proved to be an effective means for reducing the sampling rate in the projection view angle in computed tomography (CT). Most of the image reconstruction algorithms, developed for this purpose, solve a nonsmooth convex optimization problem involving the image total variation (TV). The TV seminorm is the `1 norm of the image gradient magnit...

The notion of signal sparsity has been gaining increasing interest in information theory and signal processing communities. Recent advances in fields like signal compression, sampling and analysis have accentuated the crucial role of sparse representations of signals. As a consequence, there is a strong need to measure sparsity and towards this end, a plethora of metrics has been presented in t...

A recent challenge in data analysis for science and engineering is that data are often represented in a structured way. In particular, many data mining tasks have to deal with group-structured prior information, where features or data items are organized into groups. In this paper, we develop group sparsity regularization methods for nonnegative matrix factorization (NMF). NMF is an effective d...

A nonconvex optimization algorithm is developed, which exploits gradient magnitude image (GMI) sparsity for reduction in the projection view angle sampling rate. The algorithm shows greater potential for exploiting GMI sparsity than can be obtained by convex total variation (TV) based optimization. The nonconvex algorithm is demonstrated in simulation with ideal, noiseless data for a 2D fan-bea...

The analysis of ISAR image recovery from a reduced set of data presented in [1] is extended in this correspondence to an important topic of signal nonsparsity (approximative sparsity). In real cases the ISAR images are noisy and only approximately sparse. Formula for the mean square error in the nonsparse ISAR, reconstructed under the sparsity assumption, is derived. The results are tested on e...

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional s...

SUMMARY In this overview of the recent Curvelet Reconstruction with Sparsity-promoting Inversion (CRSI) method, we present our latest 2-D and 3-D interpolation results on both synthetic and real datasets. We compare these results to interpolated data using other existing methods. Finally, we discuss the challenges related to sparsity-promoting solvers for the large-scale problems the industry f...

Extracting useful information from high-dimensional data is the focus of today’s statistical research and practice. After broad success of statistical machine learning on prediction through regularization, interpretability is gaining attention and sparsity has been used as its proxy. With the virtues of both regularization and sparsity, Lasso (L1 penalized L2 minimization) and its extensions ha...