A Fast and Sparsity-Aware Generalization of SMART for Tomographic Particle Image Velocimetry

Ioana Barbu (1) , Cédric Herzet (1)

1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences

Accessing to a fine information on tridimensional (3D) turbulent flows is typically a complex tasks that standard theoretical developments or numerical simulations fail in solving. A recent development in experimental fluid mechanics, coined Tomographic PIV (TomoPIV), aims at estimating the 3D velocity of a turbulent fluid out of a system of multiple cameras of high frequency placed around a lightly seeded flow. A crucial step in this procedure is the volume estimation of the seeded particles at each instant of the temporal sequence. An ubiquitous procedure addressing this problem in the TomoPIV literature is the Simultaneous Multiplicative Reconstruction Technique (SMART). The latter suffers from i). a slow convergence; ii). the inability to take into account additional information on the sought signal. Our contribution is twofold. First, we reveal that SMART can be seen as a nonlinear projected gradient (NPG) algorithm minimizing the Kullback-Leibler (KL) distance between the data and the signal. By doing so, we show that we can constrain SMART to account for the sparsity of the TomoPIV signal. Furthermore, we can accelerate the classical scheme to achieve a rate of decrease of the cost function scaling as O(1/k^2). A numerical assessment demonstrates the enhancement of the newly defined paradigms - that we coin (A-)SMART(\ell_1) - with respect to standard SMART in terms of quality of the reconstructed vector.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Traitement du signal et de l'image [eess.SP]

Ioana Barbu, Cédric Herzet. A Fast and Sparsity-Aware Generalization of SMART for Tomographic Particle Image Velocimetry. SPARS'15, Signal Processing with Adaptive Sparse Structured Representations, Jul 2015, Cambridge, United Kingdom. ⟨hal-01245022v2⟩