scholarly journals A Sharp Bound for the Reconstruction of Partitions

10.37236/898 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Vincent Vatter
Keyword(s):  
Reconstruction Algorithm ◽  
Sharp Bound ◽  
Integer Partition

Answering a question of Cameron, Pretzel and Siemons proved that every integer partition of $n\ge 2(k+3)(k+1)$ can be reconstructed from its set of $k$-deletions. We describe a new reconstruction algorithm that lowers this bound to $n\ge k^2+2k$ and present examples showing that this bound is best possible.

Nondestructive Inspection of Thin, Low-Z Samples using Multiplexed Compton Scatter Tomography

1997 ◽  
Vol 503 ◽  
Author(s):  
B. L. Evans ◽  
J. B. Martin ◽  
L. W. Burggraf
Keyword(s):  
Signal To Noise Ratio ◽  
Reconstruction Algorithm ◽  
Filtered Backprojection ◽  
Line Broadening ◽  
Compton Scatter ◽  
X Ray ◽  
Tomography System ◽  
Transmission Computed Tomography ◽  
High Purity Germanium ◽  
Scattered Energy

ABSTRACTThe viability of a Compton scattering tomography system for nondestructively inspecting thin, low Z samples for corrosion is examined. This technique differs from conventional x-ray backscatter NDI because it does not rely on narrow collimation of source and detectors to examine small volumes in the sample. Instead, photons of a single energy are backscattered from the sample and their scattered energy spectra are measured at multiple detector locations, and these spectra are then used to reconstruct an image of the object. This multiplexed Compton scatter tomography technique interrogates multiple volume elements simultaneously. Thin samples less than 1 cm thick and made of low Z materials are best imaged with gamma rays at or below 100 keV energy. At this energy, Compton line broadening becomes an important resolution limitation. An analytical model has been developed to simulate the signals collected in a demonstration system consisting of an array of planar high-purity germanium detectors. A technique for deconvolving the effects of Compton broadening and detector energy resolution from signals with additive noise is also presented. A filtered backprojection image reconstruction algorithm with similarities to that used in conventional transmission computed tomography is developed. A simulation of a 360–degree inspection gives distortion-free results. In a simulation of a single-sided inspection, a 5 mm × 5 mm corrosion flaw with 50% density is readily identified in 1-cm thick aluminum phantom when the signal to noise ratio in the data exceeds 28.

MICROWAVE IMAGING OF EMBEDDED OBJECT USING AN ENHANCED IMAGE RECONSTRUCTION ALGORITHM

2015 ◽  
Vol 74 (20) ◽  
pp. 1793-1801
Author(s):  
Sidi Mohammed Chouiti ◽  
Lotfi Merad ◽  
Sidi Mohammed Meriah ◽  
Xavier Raimundo
Keyword(s):  
Image Reconstruction ◽  
Reconstruction Algorithm ◽  
Microwave Imaging ◽  
Image Reconstruction Algorithm

Image Reconstruction with the Fourier Coefficients for Magnetic Induction Tomography

2020 ◽  
Vol 16 (2) ◽  
pp. 156-163
Author(s):  
Jingwen Wang ◽  
Xu Wang ◽  
Dan Yang ◽  
Kaiyang Wang
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Magnetic Induction ◽  
Fourier Coefficients ◽  
Signal Reconstruction ◽  
Reconstruction Algorithm ◽  
Reconstruction Method ◽  
Measurement Equation ◽  
Image Reconstruction Method ◽  
Magnetic Induction Tomography

Background: Image reconstruction of magnetic induction tomography (MIT) is a typical ill-posed inverse problem, which means that the measurements are always far from enough. Thus, MIT image reconstruction results using conventional algorithms such as linear back projection and Landweber often suffer from limitations such as low resolution and blurred edges. Methods: In this paper, based on the recent finite rate of innovation (FRI) framework, a novel image reconstruction method with MIT system is presented. Results: This is achieved through modeling and sampling the MIT signals in FRI framework, resulting in a few new measurements, namely, fourier coefficients. Because each new measurement contains all the pixel position and conductivity information of the dense phase medium, the illposed inverse problem can be improved, by rebuilding the MIT measurement equation with the measurement voltage and the new measurements. Finally, a sparsity-based signal reconstruction algorithm is presented to reconstruct the original MIT image signal, by solving this new measurement equation. Conclusion: Experiments show that the proposed method has better indicators such as image error and correlation coefficient. Therefore, it is a kind of MIT image reconstruction method with high accuracy.

Ultrasonic Block Compressed Sensing Imaging Reconstruction Algorithm Based on Wavelet Sparse Representation

2020 ◽  
Vol 16 (3) ◽  
pp. 262-272
Author(s):  
Guangzhi Dai ◽  
Zhiyong He ◽  
Hongwei Sun
Keyword(s):  
Compressed Sensing ◽  
Sparse Representation ◽  
Linear Array ◽  
Imaging System ◽  
Ultrasonic Imaging ◽  
Large Data ◽  
Reconstruction Algorithm ◽  
Array Transducer ◽  
Total Data ◽  
Block Compressed Sensing

Background: This study is carried out targeting the problem of slow response time and performance degradation of imaging system caused by large data of medical ultrasonic imaging. In view of the advantages of CS, it is applied to medical ultrasonic imaging to solve the above problems. Objective: Under the condition of satisfying the speed of ultrasound imaging, the quality of imaging can be further improved to provide the basis for accurate medical diagnosis. Methods: According to CS theory and the characteristics of the array ultrasonic imaging system, block compressed sensing ultrasonic imaging algorithm is proposed based on wavelet sparse representation. Results: Three kinds of observation matrices have been designed on the basis of the proposed algorithm, which can be selected to reduce the number of the linear array channels and the complexity of the ultrasonic imaging system to some extent. Conclusion: The corresponding simulation program is designed, and the result shows that this algorithm can greatly reduce the total data amount required by imaging and the number of data channels required for linear array transducer to receive data. The imaging effect has been greatly improved compared with that of the spatial frequency domain sparse algorithm.

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