An extension of the Chui–Shi frame condition to nonuniform affine operations

Abstract In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the “weak” approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90 of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.

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Infinite matrices, wavelet coefficients and frames

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171204312457 ◽

2004 ◽

Vol 2004 (67) ◽

pp. 3695-3702

Author(s):

N. A. Sheikh ◽

M. Mursaleen

Keyword(s):

Series Expansion ◽

Infinite Matrix ◽

Wavelet Coefficients ◽

Infinite Matrices ◽

Frame Condition ◽

Wavelet Series

We study the action ofAonf∈L2(ℝ)and on its wavelet coefficients, whereA=(almjk)lmjkis a double infinite matrix. We find the frame condition forA-transform off∈L2(ℝ)whose wavelet series expansion is known.

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Modulation of the Rod-And-Frame Illusion by Additional External Stimuli

Perception ◽

10.1068/p241105 ◽

1995 ◽

Vol 24 (10) ◽

pp. 1105-1118 ◽

Cited By ~ 14

Author(s):

Donatella Spinelli ◽

Gabriella Antonucci ◽

Roberta Daini ◽

Daniela Fanzon ◽

Pierluigi Zoccolotti

Keyword(s):

Visual Processing ◽

Local Processing ◽

Frame Tilt ◽

Visual Vestibular Interaction ◽

Frame Condition ◽

External Frame ◽

Global And Local ◽

External Stimuli ◽

Rod And Frame

The presence of an additional external upright frame was studied in three experiments to separate the role of visuovestibular, global, and local mechanisms in the rod-and-frame illusion (RFI). In the first experiment, carried out in a dark room, the external frame surrounded a large tilted frame. Rod-setting errors to the vertical were abolished with the additional-frame condition (at 22° inner-frame tilt) confirming earlier findings. However, small, residual direct (at 11° inner-frame tilt) and indirect effects (at 33° inner-frame tilt) were still present, indicating the persistence of global visual processing. In the second experiment, the RFI in the dark was compared with the RFI with the lights on. Turning the light on abolished the effect at 22° and 33° frame tilt; however, a small direct effect was maintained at 11° frame tilt. These two studies indicate that the addition of veridical vertical information abolishes the effect owing to visuovestibular mechanisms. In the third experiment, a small rod and frame was used with the lights on (a condition abolishing visual—vestibular interaction). In the case of a small gap between the rod and the inducing frame (a condition which maximises local processing), the effect of the outer upright frame was negligible; this indicates that the additional frame had no effect on local processing. In the case of a large gap (a condition which minimises local processing), the external square reduced the illusion, indicating its modulating effect on visual global processing. Overall, an upright external frame exerts a differential influence depending on which mechanisms contribute most to the RFI in a given experimental condition.

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Observations on Stroboscopic Induced Motion

Perception ◽

10.1068/p160061 ◽

1987 ◽

Vol 16 (1) ◽

pp. 61-72

Author(s):

Francesco Micella ◽

Baingio Pinna

Keyword(s):

Interstimulus Interval ◽

Stimulus Display ◽

Median Plane ◽

Relative Displacement ◽

Frame Condition ◽

Induced Motion ◽

The Subject ◽

Perceived Velocity ◽

Determining Factor ◽

Object Frame

Subject-relative explanations of motion induction state that induced motion is the result of a misperceived shift of the median plane of the visual field of the subject. This theory does not require relative motion of the spot and frame, in the classical spot-and-frame condition, only asymmetrical stimulation. Three experiments are reported in which stroboscopic induced motion was investigated. The experimental arrangement was unconventional in that the induced object (spot) was presented only during the interstimulus interval between the exposures of the inducing object (frame). This allowed differentiation of the duration of the induced movement and that of the inducing one. In the first experiment it was demonstrated that perception of induced motion depends upon the duration of the interstimulus interval between the presentations of the inducing frame. In the second experiment it was shown that the perceived velocity of the induced movement can be different from that of the inducing one and depends on the duration of exposure of the induced object. In the third experiment a stimulus display was created in which the apparent displacement of an object and its induced motion are incongruous. The results are incompatible with subject-relative displacement as the sole determining factor of motion induction and they present some difficulties for the hypothesis that induced motion is the result of the apportionment of the objective displacement of the frame.

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Multivariate Gabor frames for operators in matrix-valued signal spaces over locally compact abelian groups

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691320500691 ◽

2020 ◽

pp. 2050069

Author(s):

Divya Jindal ◽

Uttam Kumar Sinha ◽

Geetika Verma

Keyword(s):

Sufficient Conditions ◽

Gabor Frame ◽

Gabor Frames ◽

Locally Compact ◽

Bounded Linear ◽

Frame Condition ◽

Compact Abelian Groups ◽

Lower Frame ◽

Necessary And Sufficient ◽

Lca Groups

In this paper, we study multivariate Gabor frames in matrix-valued signal spaces over locally compact abelian (LCA) groups, where the lower frame condition depends on a bounded linear operator [Formula: see text] on the underlying matrix-valued signal space. This type of Gabor frame is also known as a multivariate [Formula: see text]-Gabor frame. By extending work of Gǎvruta, we present necessary and sufficient conditions for the existence of [Formula: see text]-Gabor frames of multivariate matrix-valued Gabor systems. Some operators which can transform multivariate matrix-valued Gabor and [Formula: see text]-Gabor frames into [Formula: see text]-Gabor frames in terms of adjointable operators are discussed. Finally, we give a Paley–Wiener-type perturbation result for multivariate matrix-valued [Formula: see text]-Gabor frames.

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WEIGHTED AND CONTROLLED FRAMES: MUTUAL RELATIONSHIP AND FIRST NUMERICAL PROPERTIES

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691310003377 ◽

2010 ◽

Vol 08 (01) ◽

pp. 109-132 ◽

Cited By ~ 36

Author(s):

PETER BALAZS ◽

JEAN-PIERRE ANTOINE ◽

ANNA GRYBOŚ

Keyword(s):

Iterative Algorithms ◽

Gabor Frames ◽

Dual Frame ◽

Mutual Relationship ◽

Frame Operator ◽

Numerical Efficiency ◽

Frame Condition ◽

Frame Bound ◽

Special Case ◽

Numerical Advantage

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while offering a numerical advantage in the sense of preconditioning. Next, we investigate weighted frames, in particular their relation to controlled frames. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers. Finally, we analyze weighted frames numerically. First, we investigate three possibilities for finding weights in order to tighten a given frame, i.e. decrease the frame bound ratio. Then, we examine Gabor frames and how well the canonical dual of a weighted frame is approximated by the inversely weighted dual frame.

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The Effect of a Goal-Framing Manipulation on Environmentalism

10.31219/osf.io/vuyhc ◽

2020 ◽

Author(s):

Teaghan Hogg ◽

Samantha Stanley

Keyword(s):

Political Orientation ◽

Environmental Action ◽

Goal Framing ◽

Main Effect ◽

Frame Condition

We promoted pro-environmental action as aligned with hedonic, gain and normative goal-frames to test the influence on liberal and conservative environmentalism. Environmentalism was not affected by goal-frame condition, but a main effect of political orientation showed liberals reported greater climate belief and willingness to take action. Overall, frames were equally (in)effective, regardless of political leaning.

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Attention, frame condition, and decision making under risk: An empirical test of the Contingent Focus Model using an eye gaze recorder

PsycEXTRA Dataset ◽

10.1037/e683332011-067 ◽

2003 ◽

Cited By ~ 3

Author(s):

Satoshi Fujii ◽

Kazuhisa Takemura

Keyword(s):

Decision Making ◽

Empirical Test ◽

Eye Gaze ◽

Decision Making Under Risk ◽

Frame Condition

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Individual Differences in Risk-Taking Tendency and Framing Effect

Social Behavior and Personality An International Journal ◽

10.2224/sbp.2014.42.2.279 ◽

2014 ◽

Vol 42 (2) ◽

pp. 279-284 ◽

Cited By ~ 2

Author(s):

Gang Huangfu

Keyword(s):

Individual Differences ◽

Reaction Time ◽

Risk Taking ◽

Framing Effect ◽

Frame Condition ◽

The Relationship

I investigated the relationship between framing effect and individuals' level of tendency to take risks. The results showed that the strength of the tendency of individuals to take risks influences the occurrence of framing effect. Frame had relatively less impact on those participants whose tendency to take risks was stronger than that of other people and people in this group tended to pursue risks in both positive and negative frame conditions. Frame had a stronger impact on those participants with a weaker risk-taking tendency, and they tended to avoid risks under positive framing conditions but pursued risks under negative framing. These results explain the preference shift phenomenon, whereby a tendency to take risks under a positive framing condition becomes stronger under a negative framing condition (unidirectional framing effect), that has been found in previous studies. The results also confirmed that framing influenced participants' reaction time, which was shorter in the positive frame condition than in the negative frame condition.

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Dispositional Self-Confidence in Judgment and Framing Bias Susceptibility in a Dynamic Decision Making Environment

Proceedings of the Human Factors and Ergonomics Society Annual Meeting ◽

10.1177/107118139704100157 ◽

1997 ◽

Vol 41 (1) ◽

pp. 249-253

Author(s):

Thomas E. Nygren ◽

Terry Ransom-Flint

Keyword(s):

Decision Making ◽

Past Research ◽

Flight Simulation ◽

Dynamic Decision Making ◽

Actual Performance ◽

Self Confidence ◽

High Workload ◽

Frame Condition ◽

Decision Making Behavior ◽

The Impact

Decision-makers demonstrate framing bias when their decision making behavior is a function of the contextual presentation or framing (positive or negative) of the decision problem. Framing effects in simple, static situations (e.g., gambling) have been well documented, but past research on framing has typically ignored both dynamic environments and the effects of predispositional variables like risk-taking tendency and confidence in judgment. We examined the impact of these influences by exposing participants who measured either very high or low in decision making self-confidence to a high workload environment with either an “opportunity for gain” or a “threat of loss” decision frame condition. Participants performed a multi-task, computer-generated flight simulation program (the MAT) for 30 minutes. Results indicated that participants' actual performance on the MAT subtasks could be affected by the framing manipulation, and also that their decision strategies to optimize task performance were influenced by both by the framing manipulation and their self-confidence level.

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