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Dictionary Methods for Compressed Sensing: Framework for Microscopy
Published in Jeffrey P. Simmons, Lawrence F. Drummy, Charles A. Bouman, Marc De Graef, Statistical Methods for Materials Science, 2019
Saiprasad Ravishankar, R. Rao Nadakuditi
Techniques exploiting sparsity have become extremely popular in various imaging and image processing applications in recent years. These techniques typically use the sparsity of images or image patches in a transform domain or dictionary to compress [638], denoise, or restore/reconstruct images. Compressed sensing (CS) is a method that enables accurate reconstruction of images from a few measurements by exploiting the sparsity of the images in a known transform domain or dictionary. CS has been recently used in applications such as materials science microscopy and enables dose reduction and accelerated data acquisition. In this chapter, we focus on adaptive dictionary methods and discuss the approach of blind compressed sensing (BCS), which aims to reconstruct images in the scenario when a good sparse model for the image is unknown a priori. BCS allows the dictionary to be adaptive to the underlying images, leading to sparser image representations and better image reconstructions from few measurements. In the following, we briefly review the synthesis dictionary model and its learning, CS, and BCS.
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Published in Mara Cercignani, Nicholas G. Dowell, Paul S. Tofts, Quantitative MRI of the Brain: Principles of Physical Measurement, 2018
Wieland A. Worthoff, Aliaksandra Shymanskaya, Chang-Hoon Choi, Jörg Felder, Ana-Maria Oros-Peusquens, N. Jon Shah
TSC sequences often employ gradient echo techniques; however, modern non-Cartesian acquisition schemes allow one to acquire signal without generation of an echo, which leads to high signal-to-noise ratio (SNR) and short acquisition times (Shah et al., 2016). Different k-space sampling schemes using twisted projection imaging (TPI) and density-adapted 3D-projection reconstruction imaging methods also improve SNR (Konstandin and Nagel, 2014). However, TPI was proven to be a more robust technique at high fields for 23Na concentration mapping compared to (radial) gradient echo (GRE) or density adapted radial imaging (Romanzetti et al., 2006). TPI-SENSE is a combination of TPI trajectories with sensitivity encoding techniques (Qian et al., 2009). Madelin et al. (2012) demonstrated that compressed sensing can lead to a reduction in acquisition time, without significant image quality reduction. For imaging of the intra- and extracellular sodium signals, multiple quantum filtering can be used (Keltner et al., 1994), which usually consist of three hard pulses (Chung and Wimperis, 1990) and adheres to a scheme that isolates multi–quantum filtered signal contributions, such as multiplex phase cycling (Ivchenko et al., 2003). The SISTINA sequence allows simultaneous acquisition of single and triple quantum coherences (Fiege et al., 2013a).
Chapter 11: Miscellaneous Topics Used for Engineering Problems
Published in Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene, Modern Engineering Mathematics, 2017
Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene
Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Shannon-Nyquist sampling theorem. There are two conditions under which recovery is possible. The first one requires the signal to be sparse in some domain. The second one is incoherence which is applied through the isometric property which is sufficient for sparse signals.
Research on the modulation factor of the constrained TV for optical deflection tomography reconstruction
Published in Inverse Problems in Science and Engineering, 2020
Huaxin Li, Bin Zhang, Huihua Kong, Jinxiao Pan
Compressed sensing can reconstruct signals from a small amount of projection data. Reconstruction is the process of finding the sparsest solution under the conditions that satisfy the observation value. If the image or distribution matrix is represented by , then the projection observation value is expressed as , represents a sparse transformation, and the projection matrix is represented by, where and are irrelevant. The original distribution can be reconstructed by solving Equation (7). where the zero norm denotes the number of non-zero elements. Formula (7) is a typical non-convex optimization problem. Because the solving process of this problem is rather difficult, Candes and Donoho proposed to use norm instead of norm [14,24], then formula (7) becomes formula (8) where , the above formula (8) can be transformed into convex optimization problem to solve. In order to make the solutions of formula (7) and formula (8) equivalent, the coefficient matrix and the perception matrix must be irrelevant.
3D LiDAR point cloud image codec based on Tensor
Published in The Imaging Science Journal, 2020
PL. Chithra, A. Christoper Tamilmathi
Compressed sensing has demanded significant attention in the areas of applied mathematics, computer science, and signal processing in recent years. One major task in compressed sensing is to retrieve a signal from relatively few measurements using a sparse optimization technique. A sparse optimization method is to find a sparse solution from all feasible solutions of a problem [6]. The preprocessed image is reshaped as square sized (3 × 3) non-overlapping blocks. These blocks are two-dimensional sections of an image. Each signal block is decomposed into even and odd signal components. An odd signal from the first-level decomposition is again decomposed into even and odd components. The second level of the odd signal has been retained for the next process since it contains high informative elements than the even (lesser significant) component.
A robust compressed sensing image encryption algorithm based on GAN and CNN
Published in Journal of Modern Optics, 2022
Xiuli Chai, Ye Tian, Zhihua Gan, Yang Lu, Xiang-Jun Wu, Guoqiang Long
With the development of the Internet and big data, enormous number of images need to be stored and transmitted through the Internet. To reduce the cost of transmission and storage, it is very necessary to compress the image. Unlike the traditional compression methods of sampling before compression, the emergence of compressed sensing [1,2] makes sampling and compression integrated. Because the number of measurements required is much less than that of Nyquist theory [3], compressed sensing technology is widely used in many practical fields, including single pixel camera [4,5], compressed magnetic resonance imaging [6,7], snapshot hyperspectral imaging, image compression encryption [8,9], etc.