FFT multichannel interpolation and application to image super-resolution

Dong, Cheng; Kou, Kit Ian

doi:10.1016/j.sigpro.2019.03.025

Cited by 18 publications

(8 citation statements)

References 52 publications

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“…In an ideal interpolation, given the appropriate conditions, a continuous signal can be exactly reconstructed from the discrete points [CHE19]. A spatial interpolation can predict the values of the unknown points by processing the surrounding variables with meaningful values within the same region.…”

Section: Fundamental Concepts Of Data Interpolationmentioning

confidence: 99%

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nfluence of Measuring Points in Ultrasonic Tests on the Tomographic Image Quality of Concrete

Moura¹,

Carvalho²,

Ferreira³

2020

Computer Science Research Notes

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In the process of creating digital images of concrete, wave propagation can be used to generate a suitable inner representation of this element, producing an ultrasonic tomography. Although tomography devices are efficient in generating images, they are high-cost and not very accessible. On the other hand, images obtained through ultrasound tests allow identifying the presence of flaws in different types of materials at lower costs. In ultrasonic tests, ultrasonic wave velocity paths are generated from different measurement points. Thus, in order to improve the data range, interpolation techniques can be used to estimate the acoustic velocity at the unmeasured test points, completing the image creation process. This work aims to evaluate the influence on the quality of the generated image of (1) the spatial resolution and (2) the number of measurement points in the ultrasonic test. Experiments were carried out using Inverse Distance Weighting interpolation technique and ultrasonic tomography on concrete beams with and without flaws. The resulting images indicated the importance of the appropriate choice of number and arrangement of measuring points in the ultrasonic test to properly detect internal flaws. In addition, we verify that a higher spatial resolution may also interfere in the identification of internal flaws in the image.

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Section: Fundamental Concepts Of Data Interpolationmentioning

confidence: 99%

“…By means of the interpolation technique it is possible to reconstruct or approximate the continuous signals from a series of discrete points [CHE19]. This technique has been widely applied to super-resolution and im-1 age reconstruction in ultrasonic tomography [DON16] [FAN17] [FAN18].…”

Section: Introductionmentioning

confidence: 99%

nfluence of Measuring Points in Ultrasonic Tests on the Tomographic Image Quality of Concrete

Moura¹,

Carvalho²,

Ferreira³

2020

Computer Science Research Notes

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“…Certain studies have been given to the sampling theorems for the periodic bandlimited functions [10,11]. Moreover, the multichannel sampling approach has been extended to the time-limited functions [12].…”

Section: Introductionmentioning

confidence: 99%

“…And the matrix involved in this inverse problem may have a large condition number if the sample sets {g m ( 2πp L ), 0 ≤ p ≤ L − 1}, 1 ≤ m ≤ M have a high degree of relevance. In spite of this, in [8,12], the authors showed that the large scale (N s ) inverse problem could be converted to a simple inversion problem of small matrices (M × M ) by partitioning the frequency band into small pieces. Moreover, the closed-form of the MCI formula as well as the FFT-based implementation algorithm (see Algorithm 1) were provided.…”

Section: Introductionmentioning

confidence: 99%

Signal reconstruction from noisy multichannel samples

Chen¹,

Hu²,

Kou³

2022

Preprint

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We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is inappropriate. Thus the reasonable smoothing and regularized corrections are indispensable. In this paper, we propose several alternative methods for the signal reconstruction from the noisy multichannel samples under different smoothing and regularization principles. We compare these signal reconstruction methods theoretically and experimentally in the various situations. To demonstrate the effectiveness of the proposed methods, the probability interpretation and the error analysis for these methods are provided. Additionally, the numerical simulations as well as some guidelines to use the methods are also presented.

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“…To address the above difficulty, the low resolution images are first upsampled. Then, the upsampled images are processed via the lowpass interpolation filters [5]. Since the upsampling operation and the lowpass filtering are the linear operators, the obtained performances are limited by these linear operators.…”

Section: Introductionmentioning

confidence: 99%

Joint 2D SSA with GSVD and binary linear programming based image super-resolution

Huang

Chan

Ling

et al. 2021

Preprint

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This paper proposes a joint two dimensional (2D) singular spectrum analysis (SSA) with the generalized singular value decomposition (GSVD) and the binary linear programming based method for performing the super-resolution. For a given low resolution image, first both the upsampling operation and a lowpass filtering are applied on each column of the image to obtain an enlarged image. Second, apply the 2D Hankelization to both the low resolution image and the enlarged image to obtain their corresponding trajectory matrices. Third, both the GSVD and the 2D de-Hankelization are applied to these two trajectory matrices to obtain their corresponding sets of the de-Hankelized 2D SSA components. Here, it is proved that the exact perfect reconstruction is achieved. In order to enhance the high frequency contents of the enlarged image, the selection of the de-Hankelized 2D SSA components is formulated as a binary linear programming problem. Computer numerical simulation results show that the proposed method outperforms the state of art methods.

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FFT multichannel interpolation and application to image super-resolution

Cited by 18 publications

References 52 publications

nfluence of Measuring Points in Ultrasonic Tests on the Tomographic Image Quality of Concrete

nfluence of Measuring Points in Ultrasonic Tests on the Tomographic Image Quality of Concrete

Signal reconstruction from noisy multichannel samples

Joint 2D SSA with GSVD and binary linear programming based image super-resolution

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