242 research outputs found
The Application of Preconditioned Alternating Direction Method of Multipliers in Depth from Focal Stack
Post capture refocusing effect in smartphone cameras is achievable by using
focal stacks. However, the accuracy of this effect is totally dependent on the
combination of the depth layers in the stack. The accuracy of the extended
depth of field effect in this application can be improved significantly by
computing an accurate depth map which has been an open issue for decades. To
tackle this issue, in this paper, a framework is proposed based on
Preconditioned Alternating Direction Method of Multipliers (PADMM) for depth
from the focal stack and synthetic defocus application. In addition to its
ability to provide high structural accuracy and occlusion handling, the
optimization function of the proposed method can, in fact, converge faster and
better than state of the art methods. The evaluation has been done on 21 sets
of focal stacks and the optimization function has been compared against 5 other
methods. Preliminary results indicate that the proposed method has a better
performance in terms of structural accuracy and optimization in comparison to
the current state of the art methods.Comment: 15 pages, 8 figure
Forward-Backward Splitting in Deformable Image Registration: A Demons Approach
Efficient non-linear image registration implementations are
key for many biomedical imaging applications. By using the
classical demons approach, the associated optimization problem
is solved by an alternate optimization scheme consisting
of a gradient descent step followed by Gaussian smoothing.
Despite being simple and powerful, the solution of the underlying
relaxed formulation is not guaranteed to minimize
the original global energy. Implicitly, however, this second
step can be recast as the proximal map of the regularizer.
This interpretation introduces a parallel to the more general
Forward-Backward Splitting (FBS) scheme consisting of a
forward gradient descent and proximal step. By shifting entirely
to FBS, we can take advantage of the recent advances in
FBS methods and solve the original, non-relaxed deformable
registration problem for any type of differentiable similarity
measure and convex regularization associated with a tractable
proximal operator. Additionally, global convergence to a
critical point is guaranteed under weak restrictions. For the
first time in the context of image registration, we show that
Tikhonov regularization breaks down to the simple use of
B-Spline filtering in the proximal step. We demonstrate the
versatility of FBS by encoding spatial transformation as displacement
fields or free-form B-Spline deformations. We use
state-of-the-art FBS solvers and compare their performance
against the classical demons, the recently proposed inertial
demons and the conjugate gradient optimizer. Numerical experiments
performed on both synthetic and clinical data show
the advantage of FBS in image registration in terms of both
convergence and accuracy
A Multi-Grid Iterative Method for Photoacoustic Tomography
Inspired by the recent advances on minimizing nonsmooth or bound-constrained
convex functions on models using varying degrees of fidelity, we propose a line
search multigrid (MG) method for full-wave iterative image reconstruction in
photoacoustic tomography (PAT) in heterogeneous media. To compute the search
direction at each iteration, we decide between the gradient at the target
level, or alternatively an approximate error correction at a coarser level,
relying on some predefined criteria. To incorporate absorption and dispersion,
we derive the analytical adjoint directly from the first-order acoustic wave
system. The effectiveness of the proposed method is tested on a total-variation
penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated
variant (FISTA), which have been used in many studies of image reconstruction
in PAT. The results show the great potential of the proposed method in
improving speed of iterative image reconstruction
Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion Estimation
A crucial limitation of current high-resolution 3D photoacoustic tomography
(PAT) devices that employ sequential scanning is their long acquisition time.
In previous work, we demonstrated how to use compressed sensing techniques to
improve upon this: images with good spatial resolution and contrast can be
obtained from suitably sub-sampled PAT data acquired by novel acoustic scanning
systems if sparsity-constrained image reconstruction techniques such as total
variation regularization are used. Now, we show how a further increase of image
quality can be achieved for imaging dynamic processes in living tissue (4D
PAT). The key idea is to exploit the additional temporal redundancy of the data
by coupling the previously used spatial image reconstruction models with
sparsity-constrained motion estimation models. While simulated data from a
two-dimensional numerical phantom will be used to illustrate the main
properties of this recently developed
joint-image-reconstruction-and-motion-estimation framework, measured data from
a dynamic experimental phantom will also be used to demonstrate their potential
for challenging, large-scale, real-world, three-dimensional scenarios. The
latter only becomes feasible if a carefully designed combination of tailored
optimization schemes is employed, which we describe and examine in more detail
Blur resolved OCT: full-range interferometric synthetic aperture microscopy through dispersion encoding
We present a computational method for full-range interferometric synthetic
aperture microscopy (ISAM) under dispersion encoding. With this, one can
effectively double the depth range of optical coherence tomography (OCT),
whilst dramatically enhancing the spatial resolution away from the focal plane.
To this end, we propose a model-based iterative reconstruction (MBIR) method,
where ISAM is directly considered in an optimization approach, and we make the
discovery that sparsity promoting regularization effectively recovers the
full-range signal. Within this work, we adopt an optimal nonuniform discrete
fast Fourier transform (NUFFT) implementation of ISAM, which is both fast and
numerically stable throughout iterations. We validate our method with several
complex samples, scanned with a commercial SD-OCT system with no hardware
modification. With this, we both demonstrate full-range ISAM imaging, and
significantly outperform combinations of existing methods.Comment: 17 pages, 7 figures. The images have been compressed for arxiv -
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