1,658 research outputs found
A Theoretically Guaranteed Deep Optimization Framework for Robust Compressive Sensing MRI
Magnetic Resonance Imaging (MRI) is one of the most dynamic and safe imaging
techniques available for clinical applications. However, the rather slow speed
of MRI acquisitions limits the patient throughput and potential indi cations.
Compressive Sensing (CS) has proven to be an efficient technique for
accelerating MRI acquisition. The most widely used CS-MRI model, founded on the
premise of reconstructing an image from an incompletely filled k-space, leads
to an ill-posed inverse problem. In the past years, lots of efforts have been
made to efficiently optimize the CS-MRI model. Inspired by deep learning
techniques, some preliminary works have tried to incorporate deep architectures
into CS-MRI process. Unfortunately, the convergence issues (due to the
experience-based networks) and the robustness (i.e., lack real-world noise
modeling) of these deeply trained optimization methods are still missing. In
this work, we develop a new paradigm to integrate designed numerical solvers
and the data-driven architectures for CS-MRI. By introducing an optimal
condition checking mechanism, we can successfully prove the convergence of our
established deep CS-MRI optimization scheme. Furthermore, we explicitly
formulate the Rician noise distributions within our framework and obtain an
extended CS-MRI network to handle the real-world nosies in the MRI process.
Extensive experimental results verify that the proposed paradigm outperforms
the existing state-of-the-art techniques both in reconstruction accuracy and
efficiency as well as robustness to noises in real scene
Universal Approach to Overcoming Nonstationarity, Unsteadiness and Non-Markovity of Stochastic Processes in Complex Systems
In present paper we suggest a new universal approach to study complex systems
by microscopic, mesoscopic and macroscopic methods. We discuss new
possibilities of extracting information on nonstationarity, unsteadiness and
non-Markovity of discrete stochastic processes in complex systems. We consider
statistical properties of the fast, intermediate and slow components of the
investigated processes in complex systems within the framework of microscopic,
mesoscopic and macroscopic approaches separately. Among them theoretical
analysis is carried out by means of local noisy time-dependent parameters and
the conception of a quasi-Brownian particle (QBP) (mesoscopic approach) as well
as the use of wavelet transformation of the initial row time series. As a
concrete example we examine the seismic time series data for strong and weak
earthquakes in Turkey () in detail, as well as technogenic
explosions. We propose a new way of possible solution to the problem of
forecasting strong earthquakes forecasting. Besides we have found out that an
unexpected restoration of the first two local noisy parameters in weak
earthquakes and technogenic explosions is determined by exponential law. In
this paper we have also carried out the comparison and have discussed the
received time dependence of the local parameters for various seismic phenomena
Image Restoration Using Joint Statistical Modeling in Space-Transform Domain
This paper presents a novel strategy for high-fidelity image restoration by
characterizing both local smoothness and nonlocal self-similarity of natural
images in a unified statistical manner. The main contributions are three-folds.
First, from the perspective of image statistics, a joint statistical modeling
(JSM) in an adaptive hybrid space-transform domain is established, which offers
a powerful mechanism of combining local smoothness and nonlocal self-similarity
simultaneously to ensure a more reliable and robust estimation. Second, a new
form of minimization functional for solving image inverse problem is formulated
using JSM under regularization-based framework. Finally, in order to make JSM
tractable and robust, a new Split-Bregman based algorithm is developed to
efficiently solve the above severely underdetermined inverse problem associated
with theoretical proof of convergence. Extensive experiments on image
inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise
removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions
on Circuits System and Video Technology (TCSVT). High resolution pdf version
and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal
Unveiling meaningful geophysical information from seismic data requires to
deal with both random and structured "noises". As their amplitude may be
greater than signals of interest (primaries), additional prior information is
especially important in performing efficient signal separation. We address here
the problem of multiple reflections, caused by wave-field bouncing between
layers. Since only approximate models of these phenomena are available, we
propose a flexible framework for time-varying adaptive filtering of seismic
signals, using sparse representations, based on inaccurate templates. We recast
the joint estimation of adaptive filters and primaries in a new convex
variational formulation. This approach allows us to incorporate plausible
knowledge about noise statistics, data sparsity and slow filter variation in
parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a
constrained minimization problem that alleviates standard regularization issues
in finding hyperparameters. The approach demonstrates significantly good
performance in low signal-to-noise ratio conditions, both for simulated and
real field seismic data
Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow
This paper considers the noisy sparse phase retrieval problem: recovering a
sparse signal from noisy quadratic measurements , , with independent sub-exponential
noise . The goals are to understand the effect of the sparsity of
on the estimation precision and to construct a computationally feasible
estimator to achieve the optimal rates. Inspired by the Wirtinger Flow [12]
proposed for noiseless and non-sparse phase retrieval, a novel thresholded
gradient descent algorithm is proposed and it is shown to adaptively achieve
the minimax optimal rates of convergence over a wide range of sparsity levels
when the 's are independent standard Gaussian random vectors, provided
that the sample size is sufficiently large compared to the sparsity of .Comment: 28 pages, 4 figure
Multi-Scale Edge Detection Algorithms and Their Information-Theoretic Analysis in the Context of Visual Communication
The unrealistic assumption that noise can be modeled as independent, additive and uniform can lead to problems when edge detection methods are applied to low signal-to-noise ratio (SNR) images. The main reason for this is because the filter scale and the threshold for the gradient are difficult to determine at a regional or local scale when the noise estimate is on a global scale. Therefore, in this dissertation, we attempt to solve these problems by using more than one filter to detect the edges and discarding the global thresholding method in the edge discrimination. The proposed multi-scale edge detection algorithms utilize the multi-scale description to detect and localize edges. Furthermore, instead of using the single default global threshold, a local dynamic threshold is introduced to discriminate between edges and non-edges. The proposed algorithms also perform connectivity analysis on edge maps to ensure that small, disconnected edges are removed. Experiments where the methods are applied to a sequence of images of the same scene with different SNRs show the methods to be robust to noise. Additionally, a new noise reduction algorithm based on the multi-scale edge analysis is proposed. In general, an edgeâhigh frequency information in an imageâwould be filtered or suppressed after image smoothing. With the help of multi-scale edge detection algorithms, the overall edge structure of the original image could be preserved when only the isolated edge information that represents noise gets filtered out. Experimental results show that this method is robust to high levels of noise, correctly preserving the edges. We also propose a new method for evaluating the performance of edge detection algorithms. It is based on information-theoretic analysis of the edge detection algorithms in the context of an end-to-end visual communication channel. We use the information between the scene and the output of the edge-detection algorithm, ala Shannon, to evaluate the performance. An edge detection algorithm is considered to have high performance only if the information rate from the scene to the edge approaches the maximum possible. Therefore, this information-theoretic analysis becomes a new method to allow comparison between different edge detection operators for a given end-to-end image processing system
Semi-blind Sparse Image Reconstruction with Application to MRFM
We propose a solution to the image deconvolution problem where the
convolution kernel or point spread function (PSF) is assumed to be only
partially known. Small perturbations generated from the model are exploited to
produce a few principal components explaining the PSF uncertainty in a high
dimensional space. Unlike recent developments on blind deconvolution of natural
images, we assume the image is sparse in the pixel basis, a natural sparsity
arising in magnetic resonance force microscopy (MRFM). Our approach adopts a
Bayesian Metropolis-within-Gibbs sampling framework. The performance of our
Bayesian semi-blind algorithm for sparse images is superior to previously
proposed semi-blind algorithms such as the alternating minimization (AM)
algorithm and blind algorithms developed for natural images. We illustrate our
myopic algorithm on real MRFM tobacco virus data.Comment: This work has been submitted to the IEEE Trans. Image Processing for
possible publicatio
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