45 research outputs found
Evaluating Effect of Block Size in Compressed Sensing for Grayscale Images
Compressed sensing is an evolving methodology that enables sampling at sub-Nyquist rates and still provides decent signal reconstruction. During the last decade, the reported works have suggested to improve time efficiency by adopting Block based Compressed Sensing (BCS) and reconstruction performance improvement through new algorithms. A trade-off is required between the time efficiency and reconstruction quality. In this paper we have evaluated the significance of block size in BCS to improve reconstruction performance for grayscale images. A parameter variant of BCS [15] based sampling followed by reconstruction through Smoothed Projected Landweber (SPL) technique [16] involving use of Weiner smoothing filter and iterative hard thresholding is applied in this paper. The BCS variant is used to evaluate the effect of block size on image reconstruction quality by carrying out extensive testing on 9200 images acquired from online resources provided by Caltech101 [6], University of Granada [7] and Florida State University [8]. The experimentation showed some consistent results which can improve reconstruction performance in all BCS frameworks including BCS-SPL [17] and its variants [19], [27]. Firstly, the effect of varying block size (4x4, 8x8, 16x16, 32x32 and 64x64) results in changing the Peak Signal to Noise Ratio (PSNR) of reconstructed images from at least 1 dB to a maximum of 16 dB. This challenges the common notion that bigger block sizes always result in better reconstruction performance. Secondly, the variation in reconstruction quality with changing block size is mostly dependent on the image visual contents. Thirdly, images having similar visual contents, irrespective of the size, e.g., those from the same category of Caltech101 [6] gave majority vote for the same Optimum Block Size (OBS). These focused notes may help improve BCS based image capturing at many of the existing applications. For example, experimental results suggest using block size of 8x8 or 16x16 to capture facial identity using BCS. Fourthly, the average processing time taken for BCS and reconstruction through SPL with Lapped transform of Discrete Cosine Transform as the sparifying basis remained 300 milli-seconds for block size of 4x4 to 5 seconds for block size of 64x64. Since the processing time variation remains less than 5 seconds, selecting the OBS may not affect the time constraint in many applications. Analysis reveals that no particular block size is able to provide optimum reconstruction for all images with varying nature of visual contents. Therefore, the selection of block size should be made specific to the particular type of application images depending upon their visual contents
Sparse MRI and CT Reconstruction
Sparse signal reconstruction is of the utmost importance for efficient medical imaging, conducting accurate screening for security and inspection, and for non-destructive testing. The sparsity of the signal is dictated by either feasibility, or the cost and the screening time constraints of the system. In this work, two major sparse signal reconstruction systems such as compressed sensing magnetic resonance imaging (MRI) and sparse-view computed tomography (CT) are investigated.
For medical CT, a limited number of views (sparse-view) is an option for whether reducing the amount of ionizing radiation or the screening time and the cost of the procedure. In applications such as non-destructive testing or inspection of large objects, like a cargo container, one angular view can take up to a few minutes for only one slice. On the other hand, some views can be unavailable due to the configuration of the system. A problem of data sufficiency and on how to estimate a tomographic image when the projection data are not ideally sufficient for precise reconstruction is one of two major objectives of this work. Three CT reconstruction methods are proposed: algebraic iterative reconstruction-reprojection (AIRR), sparse-view CT reconstruction based on curvelet and total variation regularization (CTV), and sparse-view CT reconstruction based on nonconvex L1-L2 regularization. The experimental results confirm a high performance based on subjective and objective quality metrics. Additionally, sparse-view neutron-photon tomography is studied based on Monte-Carlo modelling to demonstrate shape reconstruction, material discrimination and visualization based on the proposed 3D object reconstruction method and material discrimination signatures.
One of the methods for efficient acquisition of multidimensional signals is the compressed sensing (CS). A significantly low number of measurements can be obtained in different ways, and one is undersampling, that is sampling below the Shannon-Nyquist limit. Magnetic resonance imaging (MRI) suffers inherently from its slow data acquisition. The compressed sensing MRI (CSMRI) offers significant scan time reduction with advantages for patients and health care economics. In this work, three frameworks are proposed and evaluated, i.e., CSMRI based on curvelet transform and total generalized variation (CT-TGV), CSMRI using curvelet sparsity and nonlocal total variation: CS-NLTV, CSMRI that explores shearlet sparsity and nonlocal total variation: SS-NLTV. The proposed methods are evaluated experimentally and compared to the previously reported state-of-the-art methods. Results demonstrate a significant improvement of image reconstruction quality on different medical MRI datasets
Sparse and Redundant Representations for Inverse Problems and Recognition
Sparse and redundant representation of data enables the
description of signals as linear combinations of a few atoms from
a dictionary. In this dissertation, we study applications of
sparse and redundant representations in inverse problems and
object recognition. Furthermore, we propose two novel imaging
modalities based on the recently introduced theory of Compressed
Sensing (CS).
This dissertation consists of four major parts. In the first part
of the dissertation, we study a new type of deconvolution
algorithm that is based on estimating the image from a shearlet
decomposition. Shearlets provide a multi-directional and
multi-scale decomposition that has been mathematically shown to
represent distributed discontinuities such as edges better than
traditional wavelets. We develop a deconvolution algorithm that
allows for the approximation inversion operator to be controlled
on a multi-scale and multi-directional basis. Furthermore, we
develop a method for the automatic determination of the threshold
values for the noise shrinkage for each scale and direction
without explicit knowledge of the noise variance using a
generalized cross validation method.
In the second part of the dissertation, we study a reconstruction
method that recovers highly undersampled images assumed to have a
sparse representation in a gradient domain by using partial
measurement samples that are collected in the Fourier domain. Our
method makes use of a robust generalized Poisson solver that
greatly aids in achieving a significantly improved performance
over similar proposed methods. We will demonstrate by experiments
that this new technique is more flexible to work with either
random or restricted sampling scenarios better than its
competitors.
In the third part of the dissertation, we introduce a novel
Synthetic Aperture Radar (SAR) imaging modality which can provide
a high resolution map of the spatial distribution of targets and
terrain using a significantly reduced number of needed transmitted
and/or received electromagnetic waveforms. We demonstrate that
this new imaging scheme, requires no new hardware components and
allows the aperture to be compressed. Also, it
presents many new applications and advantages which include strong
resistance to countermesasures and interception, imaging much
wider swaths and reduced on-board storage requirements.
The last part of the dissertation deals with object recognition
based on learning dictionaries for simultaneous sparse signal
approximations and feature extraction. A dictionary is learned
for each object class based on given training examples which
minimize the representation error with a sparseness constraint. A
novel test image is then projected onto the span of the atoms in
each learned dictionary. The residual vectors along with the
coefficients are then used for recognition. Applications to
illumination robust face recognition and automatic target
recognition are presented
Rekonstrukcija signala iz nepotpunih merenja sa primenom u ubrzanju algoritama za rekonstrukciju slike magnetne rezonance
In dissertation a problem of reconstruction of images from undersampled measurements is considered which has direct application in creation of magnetic resonance images. The topic of the research is proposition of new regularization based methods for image reconstruction which are based on statistical Markov random field models and theory of compressive sensing. With the proposed signal model which follows the statistics of images, a new regularization functions are defined and four methods for reconstruction of magnetic resonance images are derived.У докторској дисертацији разматран је проблем реконструкције сигнала слике из непотпуних мерења који има директну примену у креирању слика магнетне резнонаце. Предмет истраживања је везан за предлог нових регуларизационих метода реконструкције коришћењем статистичких модела Марковљевог случајног поља и теорије ретке репрезентације сигнала. На основу предложеног модела који на веродостојан начин репрезентује статистику сигнала слике предложене су регуларизационе функције и креирана четири алгоритма за реконструкцију слике магнетне резонанце.U doktorskoj disertaciji razmatran je problem rekonstrukcije signala slike iz nepotpunih merenja koji ima direktnu primenu u kreiranju slika magnetne reznonace. Predmet istraživanja je vezan za predlog novih regularizacionih metoda rekonstrukcije korišćenjem statističkih modela Markovljevog slučajnog polja i teorije retke reprezentacije signala. Na osnovu predloženog modela koji na verodostojan način reprezentuje statistiku signala slike predložene su regularizacione funkcije i kreirana četiri algoritma za rekonstrukciju slike magnetne rezonance