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Jump-Sparse and Sparse Recovery Using Potts Functionals

2014
*
IEEE Transactions on Signal Processing
*

We recover

doi:10.1109/tsp.2014.2329263
fatcat:uncc7tdwzbeipdsmdvdvqwue7e
*jump*-sparse and sparse signals from blurred incomplete data corrupted by (possibly*non*-Gaussian) noise using*inverse*Potts energy functionals. ... We then propose*a*new optimization method*for*these functionals which is based on dynamic programming and*the*alternating direction method of multipliers (ADMM). ...*Theorem*2 . 2 There are linear*operators**A*and data b in L p , 1 ≤ p < ∞, such that*the*continuous time*inverse*Potts problem with respect to*A*and b does not have*a*minimizer. ...##
###
Page 3402 of Mathematical Reviews Vol. , Issue 2003e
[page]

2003
*
Mathematical Reviews
*

*A*.] (RS-SART; Saratov)

*Inverse*spectral problems

*for*singular

*non*-selfadjoint differential

*operators*with discontinuities in an interior point. ...

*For*this

*inverse*problem

*the*authors prove

*a*uniqueness

*theorem*, obtain

*a*procedure

*for*constructing

*the*solution and provide necessary and sufficient conditions

*for*

*the*solvability of

*the*

*inverse*problem ...

##
###
On the structure of the degrees of relative provability

2015
*
Israel Journal of Mathematics
*

Our work continues and greatly expands

doi:10.1007/s11856-015-1182-8
fatcat:umzkztj7djganfrwdzghrzmsty
*the*second author's paper on this topic by answering*a*number of open questions from that paper, comparing three different notions of*a**jump**operator*and studying ...*jump**inversion*as well as*the*corresponding high/low hierarchies, investigating*the*structure of true Π 0 1 -statements as*a*substructure, and connecting*the*degrees of provability to escape and domination ... Other natural questions concern*jump**inversion*. We proved*a*number of*jump**inversion**theorems*, including*the*analog of*the*Friedberg*jump**inversion**theorem**for*this structure. ...##
###
Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials

2013
*
Open Mathematics
*

AbstractWe consider Sturm-Liouville differential

doi:10.2478/s11533-013-0301-1
fatcat:27m4jcc435b2fhhfpcibs3fqd4
*operators*on*a*finite interval with discontinuous potentials having one*jump*. ... As*the*main result we obtain*a*procedure of recovering*the*location of*the*discontinuity and*the*height of*the**jump*. ... Introduction This paper is devoted to*the*numerical solution of*the**inverse*spectral problem*for*Sturm-Liouville differential*operators*with discontinuous potentials on*a*finite interval. ...##
###
The jump inversion theorem for $Q\sb{2n+1}$-degrees

1984
*
Proceedings of the American Mathematical Society
*

Assuming projective determinacy we extend Friedberg's

doi:10.1090/s0002-9939-1984-0728361-5
fatcat:4ochg54n4jdrvk72kr52ecd3em
*Jump**Inversion**theorem*to Ç2/i+i"degrees, after noticing that it fails*for**A*'2"+(-degrees. 0. Preliminaries. ...*The*set Cm is made up of A'm-degrees (*a*A'm-degree is*a*set ol reals that is an equivalence class*for**the*equivalence relation*a*=*a*", ß ö*a*E A'm(/T and ß E A'm(*a*)). ...*The*answer is yes [6] :*Jump**Inversion**theorem**for*A1,-degrees. // b > 0' then there exists an*a*such that*a*' =*a*V 0' = b. ...##
###
Linear inverse problems for Markov processes and their regularisation
[article]

2016
*
arXiv
*
pre-print

We study

arXiv:1608.04918v2
fatcat:bcskhpeux5hbdfdd34j52rntly
*the*solutions of*the**inverse*problem g(z)=∫ f(y) P_T(z,dy)*for**a*given g, where (P_t(·,·))_t ≥ 0 is*the*transition function of*a*given Markov process, X, and T is*a*fixed deterministic time, which ... to 1, and J is*a*suitably constructed*jump*process. ... Note that*the**inverse*problem given by g = Kf , where K is*a**non*-negative*operator*on*a*Hilbert space with norm less than 1, can be recast in*the*form of (1.1). ...##
###
Stability properties of a crack inverse problem in half space
[article]

2021
*
arXiv
*
pre-print

*The*highlight of this paper is showing

*a*stability result

*for*this

*inverse*problem. ... We show in this paper

*a*Lipschitz stability result

*for*

*a*crack

*inverse*problem in half space.

*The*direct problem is

*a*Laplace equation with zero Neumann condition on

*the*top boundary. ... Since

*the*injective

*operator*

*A*m 0 is compact, its

*inverse*is unbounded, so

*a*

*non*-zero lower bound

*for*

*A*m 0 h 0 L 2 (V ) has to be considered rather than

*a*lower bound

*for*h 0 H 1 0 (R) . ...

##
###
Jump inversions inside effectively closed sets and applications to randomness

2011
*
Journal of Symbolic Logic (JSL)
*

We study

doi:10.2178/jsl/1305810761
fatcat:icmx4pqznvdqrj4cg23wkknz2m
*inversions*of*the**jump**operator*on classes, combined with certain basis*theorems*. ... These*jump**inversions*have implications*for**the*study of*the**jump**operator*on*the*random degrees—*for*various notions of randomness. ... By*the*Shoenfield*jump**Inversion**theorem*[Sho59] ,*the*range of*the**jump**operator*on*the*∆ 0 2 sets is*the*class of Σ 0 2 degrees above 0 . ...##
###
Fractional normal inverse Gaussian diffusion

2011
*
Statistics and Probability Letters
*

Similarly, we show that

doi:10.1016/j.spl.2010.10.007
fatcat:cnl46zvjsbdwvp6pvu3qjaczyq
*the*NIG process,*a*Brownian motion subordinated to an*inverse*Gaussian process, is*the*limit of*a*random walk with uncorrelated*jumps*separated by i.i.d. waiting times. ... This paper shows how*the*FNIG process emerges naturally as*the*limit of*a*random walk with correlated*jumps*separated by i.i.d. waiting times. ...*A*. Kumar was supported by*a*research fellowship from*the*Council of Scientific and Industrial Research (CSIR), India. ...##
###
A Galois connection between Turing jumps and limits
[article]

2018
*
arXiv
*
pre-print

As

arXiv:1802.01355v2
fatcat:fqh5g37tfvdrtovyfxgxjpdgui
*a*monad of this pair of adjoint*operations*we obtain*a*problem that characterizes*the*low functions and dually to this another problem that characterizes*the*functions that are computable relative to ... Limit computable functions can be characterized by Turing*jumps*on*the*input side or limits on*the*output side. ... As another*non*-uniform side result of*the*limit*inversion**theorem*(*Theorem*31) we obtain*a*classical result from computability theory,*the*Friedberg*jump**inversion**theorem*[21] . ...##
###
Entropy production and fluctuations in a Maxwell's refrigerator with squeezing

2018
*
The European Physical Journal Special Topics
*

Clarifying

doi:10.1140/epjst/e2018-00093-9
fatcat:q7epdsjwpvepxlfwuo4sdzsxau
*the*impact of quantumness in*the**operation*and properties of thermal machines represents*a*major challenge. ... We study*the*validity of*the*transient entropy production fluctuation*theorem*in*the*model with and without squeezing as well as its decomposition into adiabatic and*non*-adiabatic contributions. ... ACKNOWLEDGEMENTS It is*a*pleasure to thank Juan M. R. Parrondo*for*useful comments and discussions. G. M. acknowledge funding from MINECO (Grants No. FIS2014-52486-R, No. ...##
###
Stability estimates for the fault inverse problem
[article]

2018
*
arXiv
*
pre-print

We study in this paper stability estimates

arXiv:1807.06896v1
fatcat:6ejja7646ndlxocy2xbwozdzgu
*for**the*fault*inverse*problem. In this problem, faults are assumed to be planar open surfaces in*a*half space elastic medium with known Lamé coefficients. ...*A*traction free condition is imposed on*the*boundary of*the*half space. Displacement fields present*jumps*across faults, called slips, while traction derivatives are continuous. ...*Theorem*2.2 asserts that this mapping is injective, so an*inverse**operator*can be defined. It is well known, however, that such an*operator*M is compact, therefore its*inverse*is unbounded. ...##
###
Toeplitz Operators on H 2 Spaces

1964
*
Transactions of the American Mathematical Society
*

*The*problem of invertibility

*for*I2., also using

*the*ideas of [6], was solved in 1960 by H. Widom and announced by him, in part, in [13]. ... We have solved this problem by showing that

*the*problem of invertibility of

*a*general Toeplitz

*operator*can be reduced to

*the*problem of invertibility of

*a*special type of Toeplitz

*operator*and that, in ... We shall list these below and refer to [7]

*for*

*the*proofs.

*Theorem*B. Let w be

*a*

*non*-negative function on X summable with respect to dp. ...

##
###
Toeplitz operators on $H\sp{2}$ spaces

1964
*
Transactions of the American Mathematical Society
*

*The*problem of invertibility

*for*I2., also using

*the*ideas of [6], was solved in 1960 by H. Widom and announced by him, in part, in [13]. ... We have solved this problem by showing that

*the*problem of invertibility of

*a*general Toeplitz

*operator*can be reduced to

*the*problem of invertibility of

*a*special type of Toeplitz

*operator*and that, in ... We shall list these below and refer to [7]

*for*

*the*proofs.

*Theorem*B. Let w be

*a*

*non*-negative function on X summable with respect to dp. ...

##
###
Fractional diffusion equation with distributed-order material derivative. Stochastic foundations
[article]

2015
*
arXiv
*
pre-print

Then we introduce

arXiv:1510.00315v1
fatcat:4rzaw7rplnhejbtynynsgs72du
*a*Levy walk process of distributed-order type to establish our main result, which is*the*scaling limit of*the*considered process. ... It appears that*the*probability density function of*the*scaling limit process fulfills, in*a*weak sense,*the*fractional diffusion equation with material derivative of distributed-order type. ... Acknowledgements This research was partially supported by NCN Maestro grant no. 2012/06/*A*/ST1/00258. References ...
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