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 ℓ₁ norm of the image gradient magnitude, and reducing the ℓ₁ norm is known to encourage sparsity in its argument. Recently, there has been interest in employing nonconvex ℓ_p quasinorms with 0<p<1 for sparsity exploiting image reconstruction, which is potentially more effective than ℓ₁ because nonconvex ℓ_p is closer to ℓ₀-a direct measure of sparsity. This paper develops algorithms for constrained minimization of the total p-variation (TpV), ℓ_p of the image gradient. Use of the algorithms is illustrated in the context of breast CT-an imaging modality that is still in the research phase and for which constraints on X-ray dose are extremely tight. The TpV-based image reconstruction algorithms are demonstrated on computer simulated data for exploiting gradient magnitude sparsity to reduce the projection view angle sampling. The proposed algorithms are applied to projection data from a realistic breast CT simulation, where the total X-ray dose is equivalent to two-view digital mammography. Following the simulation survey, the algorithms are then demonstrated on a clinical breast CT data set.

The availability of high-resolution digital elevation data (submeter resolution) from LiDAR has increased dramatically over the past few years. As a result, the efficient storage and transmission of those large data sets and their use for geomorphic feature extraction and hydrologic/environmental modeling are becoming a scientific challenge. This letter explores the use of multiresolution wavelet analysis for compression of LiDAR digital elevation data sets. The compression takes advantage of the fact that, in most landscapes, neighboring pixels are correlated and thus contain some redundant information. The space-frequency localization of the wavelet filters allows one to preserve detailed high-resolution features where needed while representing the rest of the landscape at lower resolution. We explore a lossy compression methodology based on biorthogonal wavelets and demonstrate that, by keeping only approximately 10% of the original information (data compression ratio ∼94%), the reconstructed landscapes retain most of the information of relevance to geomorphologic applications, such as the ability to accurately extract channel networks for environmental flux routing, as well as to identify geomorphic process transition from the curvature-slope and slope-distance relationships.