The Total Variation Regularized L1 Model for Multiscale Decomposition

Yin, Wotao; Goldfarb, Donald; Osher, Stanley

doi:10.21236/ada460529

Cited by 20 publications

(24 citation statements)

References 37 publications

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“…Note that only rough boundary locations are required for this step. First, a total variation (TV) regularized L 1 model-based decomposition [17] with regularization parameter λ = 0.01 is used to remove high-frequency details like speckle noise, but preserves information regarding location of the inner wall boundary (Figs. 3(a) and 3(b)).…”

Section: Methodsmentioning

confidence: 99%

Graph-Based IVUS Segmentation With Efficient Computer-Aided Refinement

Sun

Sonka

Beichel

2013

IEEE Trans. Med. Imaging

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A new graph-based approach for segmentation of luminal and external elastic lamina (EEL) surface of coronary vessels in gated 20 MHz intravascular ultrasound (IVUS) image sequences (volumes) is presented. The approach consists of a fully automated segmentation stage (‘new automated’ or NA) and a user-guided computer-aided refinement (‘new refinement’ or NR) stage. Both approaches are based on the LOGISMOS approach for simultaneous dual-surface graph-based segmentation. This combination allows the user to efficiently combine general information about IVUS image appearance and case-specific IVUS morphology and therefore deal with frequently occurring issues like calcified plaque – causing signal shadowing – and imaging artifacts. The automated segmentation stage starts with pre-segmenting the lumen to automatically define the lumen centerline, which is used to transform the segmentation task into a LOGISMOS-family graph optimization problem. Following the automated segmentation, the user can inspect the result and correct local or regional segmentation inaccuracies by (iteratively) providing approximate clues regarding the location of the desired surface locations. This expert information is utilized to modify the previously calculated cost functions, locally reoptimizing the underlying modified graph without a need to start the new optimization from scratch. Validation of our method was performed on 41 gated 20 MHz IVUS data sets for which an expert-defined independent standard was available. Resulting from the automated stage of the approach (NA), the mean and standard deviation of the RMS area errors for the luminal and external elastic lamina surfaces were 1.12 ± 0.67 mm2 and 2.35 ± 1.61 mm2, respectively. Following the refinement stage (NR), the RMS area errors significantly decreased to 0.82±0.44 mm2 and 1.17±0.65 mm2 for the same surfaces, respectively (p < 0.001 for both surfaces). The approach is delivering a previously unachievable speed of obtaining clinically relevant segmentations compared to the current approaches of automated segmentation followed by manual editing.

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Section: Methodsmentioning

confidence: 99%

Graph-Based IVUS Segmentation With Efficient Computer-Aided Refinement

Sun

Sonka

Beichel

2013

IEEE Trans. Med. Imaging

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“…Goldfarb and Yin [40] first reformulated this TV-regularized problem into a second-order cone programming (SOCP) setting, and the efficient interior point methods can produce an accurate solution at a polynomial computing cost. This approach has been widely used in image processing and analysis [40]–[42]. However, because the system matrix size is typically enormous in the CT field, an alternating minimization algorithm is usually chosen to solve the TV-regularized problem.…”

Section: Methodlogymentioning

confidence: 99%

Statistical Interior Tomography

Mou

Wang

et al. 2011

IEEE Trans. Med. Imaging

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This paper presents a statistical interior tomography (SIT) approach making use of compressed sensing (CS) theory. With the projection data modeled by the Poisson distribution, an objective function with a total variation (TV) regularization term is formulated in the maximization of a posteriori (MAP) framework to solve the interior problem. An alternating minimization method is used to optimize the objective function with an initial image from the direct inversion of the truncated Hilbert transform. The proposed SIT approach is extensively evaluated with both numerical and real datasets. The results demonstrate that SIT is robust with respect to data noise and down-sampling, and has better resolution and less bias than its deterministic counterpart in the case of low count data.

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“…The gradient flow for p = 1 and total variation in the continuum is related to the L 1 -TV model, which appears to have interesting multiscale properties (cf. [54]). A challenging problem is the numerical computation of eigenvalues and eigenfunctions in the nonlinear setup, which is the case also in the general case beyond the spectral clustering application.…”

Section: Cheeger Sets and Spectral Clusteringmentioning

confidence: 99%