scholarly journals Sparse Approximations of Fractional Matérn Fields

2017 ◽  
Vol 45 (1) ◽  
pp. 194-216 ◽  
Author(s):  
Lassi Roininen ◽  
Sari Lasanen ◽  
Mikko Orispää ◽  
Simo Särkkä
Keyword(s):  
Sparse Approximations

High-Performance Image Filters via Sparse Approximations

2020 ◽  
Vol 3 (2) ◽  
pp. 1-19
Author(s):  
Kersten Schuster ◽  
Philip Trettner ◽  
Leif Kobbelt
Keyword(s):  
High Performance ◽  
Hardware Acceleration ◽  
Optimization Method ◽  
Translation Invariant ◽  
Approximation Quality ◽  
Trade Offs ◽  
Sparse Approximations ◽  
Image Filters ◽  
Good Trade ◽  
And Performance

We present a numerical optimization method to find highly efficient (sparse) approximations for convolutional image filters. Using a modified parallel tempering approach, we solve a constrained optimization that maximizes approximation quality while strictly staying within a user-prescribed performance budget. The results are multi-pass filters where each pass computes a weighted sum of bilinearly interpolated sparse image samples, exploiting hardware acceleration on the GPU. We systematically decompose the target filter into a series of sparse convolutions, trying to find good trade-offs between approximation quality and performance. Since our sparse filters are linear and translation-invariant, they do not exhibit the aliasing and temporal coherence issues that often appear in filters working on image pyramids. We show several applications, ranging from simple Gaussian or box blurs to the emulation of sophisticated Bokeh effects with user-provided masks. Our filters achieve high performance as well as high quality, often providing significant speed-up at acceptable quality even for separable filters. The optimized filters can be baked into shaders and used as a drop-in replacement for filtering tasks in image processing or rendering pipelines.

scholarly journals Sparse Approximations for Quaternionic Signals

2013 ◽  
Vol 24 (2) ◽  
pp. 383-402 ◽  
Author(s):  
Quentin Barthélemy ◽  
Anthony Larue ◽  
Jérôme I. Mars
Keyword(s):  
Sparse Approximations
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