Covariance Recovery for One-Bit Sampled Data With Time-Varying Sampling Thresholds— Part II: Non-Stationary Signals

Eamaz, Arian; Yeganegi, Farhang; Soltanalian, Mojtaba

doi:10.36227/techrxiv.19224687

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…Let t 0 denote the value of t making the upper bound in (30) infimum. To prove that M T is a decreasing function in the asymptotic sample-size case (m > m ⋆ ), we use the Padé approximation (PA) which can asymptotically approximate M T with a rational function of given order through the moment matching technique as follows [24], [28], [29]:…”

Section: A Chernoff Bound Analysis For Operamentioning

confidence: 99%

One-Bit Phase Retrieval: More Samples Means Less Complexity?

Eamaz

Yeganegi

Soltanalian

2022

IEEE Trans. Signal Process.

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The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using onebit analog-to-digital converters (ADCs). A significant advantage of deploying one-bit ADCs in signal processing systems is their superior sampling rates as compared to their high-resolution counterparts. This leads to an enormous amount of one-bit samples gathered at the output of the ADC in a short period of time. We demonstrate that this advantage pays extraordinary dividends when it comes to convex phase retrieval formulationsnamely that the often encountered matrix semi-definiteness constraints as well as rank constraints (that are computationally prohibitive to enforce), become redundant for phase retrieval in the face of a growing sample size. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

show abstract

Section: A Chernoff Bound Analysis For Operamentioning

confidence: 99%

One-Bit Phase Retrieval: More Samples Means Less Complexity?

Eamaz

Yeganegi

Soltanalian

2022

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let t 0 denote the value of t making the upper bound in (30) infimum. To prove that M T is a decreasing function in the asymptotic sample-size case (m > m ⋆ ), we use the Padé approximation (PA) which can asymptotically approximate M T with a rational function of given order through the matching technique as follows [24], [28], [29]:…”

Section: A Chernoff Bound Analysis For Operamentioning

confidence: 99%

One-Bit Phase Retrieval: More Samples Means Less Complexity?

Eamaz¹,

Yeganegi²,

Soltanalian³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using one-bit analog-to-digital converters (ADCs). A significant advantage of deploying one-bit ADCs in signal processing systems is their superior sampling rates as compared to their high-resolution counterparts. This leads to an enormous amount of one-bit samples gathered at the output of the ADC in a short period of time. We demonstrate that this advantage pays extraordinary dividends when it comes to convex phase retrieval formulations-namely that the often encountered matrix semi-definiteness constraints as well as rank constraints (that are computationally prohibitive to enforce), become redundant for phase retrieval in the face of a growing sample size. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

show abstract

Section: A Chernoff Bound Analysis For Operamentioning

confidence: 99%

One-Bit Phase Retrieval: More Samples Means Less Complexity?

Eamaz¹,

Yeganegi²,

Soltanalian³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using one-bit analog-to-digital converters (ADCs). A significant advantage of deploying one-bit ADCs in signal processing systems is their superior sampling rates as compared to their high-resolution counterparts. This leads to an enormous amount of one-bit samples gathered at the output of the ADC in a short period of time. We demonstrate that this advantage pays extraordinary dividends when it comes to convex phase retrieval formulations—namely that the often encountered matrix semi-definiteness constraints as well as rank constraints (that are computationally prohibitive to enforce), become redundant for phase retrieval in the face of a growing sample size. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies

show abstract

Covariance Recovery for One-Bit Sampled Data With Time-Varying Sampling Thresholds— Part II: Non-Stationary Signals

Cited by 3 publications

References 20 publications

One-Bit Phase Retrieval: More Samples Means Less Complexity?

One-Bit Phase Retrieval: More Samples Means Less Complexity?

One-Bit Phase Retrieval: More Samples Means Less Complexity?

One-Bit Phase Retrieval: More Samples Means Less Complexity?

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