On Block Matrices Associated with Discrete Trigonometric Transforms and Arising in Wave Propagation Theory

Tsitsas, Nikolaos L.

doi:10.4208/jcm.1004-m3193

Cited by 12 publications

(3 citation statements)

References 19 publications

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“…Let us first consider the DCT-II, which belongs to the family of discrete trigonometric transforms (DTT), and their implicit extension properties [32][33][34][35][36][37][38][39][40]. To summarize the DTT sequence extensions, two relevant parameters must be considered-the symmetry type (ST) and the point of symmetry (PoS).…”

Section: A Note On the Implicit Extension Of The Sequences Depending mentioning

confidence: 99%

Automatic Classification of Morphologically Similar Fish Species Using Their Head Contours

2020

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This work deals with the task of distinguishing between different Mediterranean demersal species of fish that share a remarkably similar form and that are also used for the evaluation of marine resources. The experts who are currently able to classify these types of species do so by considering only a segment of the contour of the fish, specifically its head, instead of using the entire silhouette of the animal. Based on this knowledge, a set of features to classify contour segments is presented to address both a binary and a multi-class classification problem. In addition to the difficulty present in successfully discriminating between very similar forms, we have the limitation of having small, unreliably labeled image data sets. The results obtained were comparable to those obtained by trained experts.

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Section: A Note On the Implicit Extension Of The Sequences Depending mentioning

confidence: 99%

Automatic Classification of Morphologically Similar Fish Species Using Their Head Contours

2020

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“…A well‐known orthonormal basis is the complex‐valued discrete Fourier matrix (Strang 1997; Oppenheim 1999; Soubaras 2006). A real‐valued alternative to the Fourier basis is the Hartley basis (Strang 1997; Tsitsas 2010). The Hartley encoding matrix is defined as, where m is the shot‐index, n is the encoding index, and ℘ is the periodization index (Soubaras 2006).…”

Section: Shot‐encoding Schemesmentioning

confidence: 99%

A comparison of shot‐encoding schemes for wave‐equation migration

Godwin

Sava

2013

Geophysical Prospecting

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A B S T R A C TIn the last decade the seismic imaging industry has begun collecting data volumes with a substantial amount of data redundancy through new acquisition geometries including: wide-azimuth, rich-azimuth and full-azimuth geometries. The increased redundancy significantly improves image quality in areas with complex geology, but requires considerably greater computational power to construct an image because of the additional data and the need to use advanced imaging algorithms. One way to reduce the computational cost of processing such datasets is to blend shot-records, using shot-encoding, together prior to imaging which reduces the number of migrations necessary for imaging. The downside to doing so is that blending introduces strong, non-physical, cross-talk noise into the final image. By carefully choosing the shot-encoding scheme, we can reduce the additional noise inserted into the image and maximally reduce the number of migrations necessary. We describe a theory of blended imaging that explains all shot-encoding schemes, and use the theory to design a new class of encodings that use amplitude weights instead of phase-shifts or time-delays. We are able to use amplitude encoding to produce blended images of the same quality as previous encoding schemes at a similiar computational cost. Furthermore, we compare the results of amplitude encoding with the results from well-known shot-encoding schemes from previous work including: plane-wave migration, random-time delay, modulated-shot migration, and decimated shot-record migration. In our comparison, we find that plane-wave migration is in many ways an optimal shot-encoding scheme. However, we find that plane-wave migration produces results that are comparable to decimated shot-record migration when the total cost of imaging is taken into account, thereby calling into question the utility of shotencoding in general. Overall, this work questions the potential for shot-encoding in standard (shot-record) seismic imaging because blended imaging does not appear to sufficiently reduce the cost of imaging given the quality of the blended image compared to decimated shot-record migration..

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“…In addition, in [19], the authors propose an efficient method for the inversion of matrices with U -diagonalizable blocks (being U a fixed unitary matrix) by utilizing the U -diagonalization of each block and subsequently a similarity transformation procedure. This approach allows getting the inverse of matrices with U -diagonalizable blocks without having to assume the invertibility of the blocks involved in the procedure, provided certain conditions met.…”

Section: Introductionmentioning

confidence: 99%

Memory-usage advantageous block recursive matrix inverse

Cosme

Fernandes

Carvalho

et al. 2018

Applied Mathematics and Computation

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The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider exchanging less memory usage for more processing time in order to enable the computation of the inverse which otherwise would be prohibitive. We propose a new algorithm to compute the inverse of block partitioned matrices with a reduced memory footprint. The algorithm works recursively to invert one block of a k×k block matrix M , with k ≥ 2, based on the successive splitting of M . It computes one block of the inverse at a time, in order to limit memory usage during the entire processing. Experimental results show that, despite increasing computational complexity, matrices that otherwise would exceed the memory-usage limit can be inverted using this technique.

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On Block Matrices Associated with Discrete Trigonometric Transforms and Arising in Wave Propagation Theory

Cited by 12 publications

References 19 publications

Automatic Classification of Morphologically Similar Fish Species Using Their Head Contours

Automatic Classification of Morphologically Similar Fish Species Using Their Head Contours

A comparison of shot‐encoding schemes for wave‐equation migration

Memory-usage advantageous block recursive matrix inverse

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