Acoustic image estimation using fast transforms

Nascimento, Vítor H.; Silva, Mateus Coelho; Masiero, Bruno

doi:10.1109/sam.2016.7569675

Cited by 6 publications

(12 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The original KAT [6] was designed for acoustic camera applications. This was latter extended to superdirective microphone algorithms in [8]. In this letter, we present two main contributions.…”

Section: Introductionmentioning

confidence: 93%

“…However, the reorganization of Kronecker products can be used to speed up any problem modeled as a matrix-vector product, as long as the matrix can be described as the Kronecker product of two smaller matrices [14]. In [8], the KAT was extended to be used with a larger group of acoustic imaging and superdirective microphone algorithms, as we show next.…”

Section: Kronecker Array Transformmentioning

confidence: 99%

“…Recapitulating, as long as we have a planar sensor array with separable geometry and we define a separable scan grid, we guarantee that the corresponding far-field manifold matrix can be decomposed as the Kronecker product of two more compact manifold matrices, which will allow a speed up in calculations, as discussed in [8]. For better comprehension, we repeat the derivation of the Adjoint Fast Transform below.…”

Section: Kronecker Array Transformmentioning

confidence: 99%

“…In this letter, we present two main contributions. First, we develop a general formulation for the KAT, which extends the derivation for superdirective microphones proposed in [8] to the original KAT for acoustic cameras. This results in a much more compact derivation than the original in [6], through the use of a new relation developed between the Kronecker [9] and the Khatri-Rao [10], [11] matrix products.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the KAT was originally only applicable to arrays with separable geometry [6]- [8]. The second main contribution we present in this letter is to relax this restriction, generalizing the KAT to deal with quasi-separable arrays, i.e., separable arrays in which some positions in the grid may be left empty.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Revisiting the Kronecker Array Transform

Masiero

Nascimento

2017

IEEE Signal Process. Lett.

Self Cite

View full text Add to dashboard Cite

It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g. an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays.

show abstract

Section: Introductionmentioning

confidence: 93%

Section: Kronecker Array Transformmentioning

confidence: 99%

Section: Kronecker Array Transformmentioning

confidence: 99%