As expected, eigenvalues of the Hessian matrix fall within a sparse range [ 22- 25, 38], thereby elucidating the stiff and sloppy directions (see Additional file 1).
Based on sparse approximation of piecewise smooth functions in frame domain, we propose a new tight frame based formulation for reconstructing a piecewise smooth surface from a sparse range data set, which is robust to both additive noise and outliers.
The numerical experiments show that the proposed approach is capable of reconstructing a piecewise smooth surface with sharp edges from sparse range data corrupted with noise and outliers.
One of the inputs required by SParSE is a range of values each parameter can take.
From the NDVI images and values, all sites in the wildlife reserve and the catchment between the years 2000 and 2009 consisted of sparse vegetation as a range of 0.1 0.5 represent sparse vegetation and >0.6 represent dense vegetation.
Not all natural signals are sparse but a wide range of natural signals can be represented sparsely in terms of a dictionary and this makes it possible to use sparsity prior on a wide range of inverse problems.
Available on bootleg compilations such as the multi-disc Making of All Things Must Pass and Songs for Patti – The Mastertape Version, the mixes demonstrate the layers of instrumentation that were combined to form the commercially released recording – ranging from a sparse backing of just guitar, bass and drums, to the larger sound following brass and slide guitar overdubs.
Since the signal x of length N range bins is a sparse vector comprising of K complex target amplitudes a k where k = 1, …, K are indices corresponding to range bins where targets are located and zero elsewhere.
Bowers et al. showed that a sparse mixture of short- and long-range NOE restraints (approximately one restraint per residue) in addition to the backbone chemical shifts enables R osetta to build models at atomic-detail accuracy (34).
Sparsity (presence of a many zero entries in a vector or matrix) has been exploited in a wide range of applications including sparse regression and statistical inference, e.g., see [21, 22].
