Upper bound of single-track Gray codes and the combined coding method of period 2n

Ifost ◽  
2013 ◽  
Author(s):  
Fan Zhang ◽  
Hengjun Zhu ◽  
Ying Li ◽  
Cheng Qiu
Keyword(s):  
Upper Bound ◽  
Gray Codes ◽  
Single Track ◽  
Period 2 ◽  
Coding Method

scholarly journals Absolute Position Coding Method for Angular Sensor—Single-Track Gray Codes

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2728 ◽  
Author(s):  
Fan Zhang ◽  
Hengjun Zhu ◽  
Kan Bian ◽  
Pengcheng Liu ◽  
Jianhui Zhang
Keyword(s):  
Coding Theory ◽  
Linear Feedback ◽  
Gray Codes ◽  
Single Track ◽  
Absolute Position ◽  
Coding Method ◽  
Position Coding ◽  
Absolute Encoder ◽  
Feedback Shift Register ◽  
Generating Sequences

Single-track Gray codes (STGCs) is a type of absolute position coding method for novel angular sensors, because it has single-track property over traditional Gray codes and mono-difference over linear feedback shift register codes. However, given that the coding theory of STGCs is incomplete, STGC construction is still a challenging task even though it has been defined for more than 20 years. Published coding theories and results on STGCs are about two types of STGC, namely, necklace and self-dual necklace ordering, which are collectively called as k-spaced head STGCs. To find a new code, three constraints on generating sequences are proposed to accelerate the searching algorithm, and the complete searching result of length-6 STGCs is initially obtained. Among the entire 132 length-6 STGCs, two novel types of STGCs with non-k-spaced heads are found, and the basic structures of these codes with the general length n are proposed and defined as twin-necklace and triplet-necklace ordering STGCs. Furthermore, d-plet-necklace ordering STGC, which unifies all the known STGCs by changing the value of d, is also defined. Finally, a single-track absolute encoder prototype is designed to prove that STGCs are as convenient as the traditional position coding methods.

Near optimal single-track Gray codes

1996 ◽  
Vol 42 (3) ◽  
pp. 779-789 ◽  
Author(s):  
T. Etzion ◽  
K.G. Paterson
Keyword(s):  
Gray Codes ◽  
Single Track

Investigating the Upper-Bound Performance of Sparse-Coding-Based Spectral Reconstruction from RGB Images

2021 ◽  
Vol 2021 (29) ◽  
pp. 19-24
Author(s):  
Yi-Tun Lin ◽  
Graham D. Finlayson
Keyword(s):  
Sparse Coding ◽  
Upper Bound ◽  
Linear Mapping ◽  
Spectral Space ◽  
Spectral Reconstruction ◽  
Image Patches ◽  
Coding Method ◽  
Rgb Images ◽  
Spectral Neighborhood ◽  
Better Than

In Spectral Reconstruction (SR), we recover hyperspectral images from their RGB counterparts. Most of the recent approaches are based on Deep Neural Networks (DNN), where millions of parameters are trained mainly to extract and utilize the contextual features in large image patches as part of the SR process. On the other hand, the leading Sparse Coding method ‘A+’—which is among the strongest point-based baselines against the DNNs—seeks to divide the RGB space into neighborhoods, where locally a simple linear regression (comprised by roughly 102 parameters) suffices for SR. In this paper, we explore how the performance of Sparse Coding can be further advanced. We point out that in the original A+, the sparse dictionary used for neighborhood separations are optimized for the spectral data but used in the projected RGB space. In turn, we demonstrate that if the local linear mapping is trained for each spectral neighborhood instead of RGB neighborhood (and theoretically if we could recover each spectrum based on where it locates in the spectral space), the Sparse Coding algorithm can actually perform much better than the leading DNN method. In effect, our result defines one potential (and very appealing) upper-bound performance of point-based SR.

Single-track Gray codes

1996 ◽  
Vol 42 (5) ◽  
pp. 1555-1561 ◽  
Author(s):  
A.P. Hiltgen ◽  
K.G. Paterson ◽  
M. Brandestini
Keyword(s):  
Gray Codes ◽  
Single Track

The structure of single-track Gray codes

1999 ◽  
Vol 45 (7) ◽  
pp. 2383-2396 ◽  
Author(s):  
M. Schwartz ◽  
T. Etzion
Keyword(s):  
Gray Codes ◽  
Single Track

Cooling Limit Approach for Single-Pulse Thermal Therapies

2004 ◽  
Author(s):  
Kung-Shan Cheng
Keyword(s):  
Closed Form ◽  
Upper Bound ◽  
Treatment Protocol ◽  
Blood Perfusion ◽  
Single Pulse ◽  
Peak Temperature ◽  
Thermal Dose ◽  
Efficient Treatment ◽  
Period 2 ◽  
Thermal Therapies

Based upon the commonly used Sapareto-Dewey thermal dose formula, a thermal treatment is divided into four periods: 1) period-1 is from 37°C to 43°C, 2) period-2 is from 43°C to Tpeak, 3) period-3 is from Tpeak to 43°C, and 4) period-4 is 43°C to 38°C. A recent study derived a closed form thermal dose formula based on a combined term, the “effective cooling frequency,” revealed that one can determine the best performance of a thermal therapy by concentrating on the cooling periods: period-3 and period-4. As an extension, this study used a closed-form temperature solution to investigate the influences from both cooling terms (perfusion and thermal conduction) separately. The results determined the upper bound of the peak temperature for pulses with different focal sizes under different blood perfusion values. Under practical settings, no pulse should introduce peak temperature higher than 67°C to avoid overdosing when the desired thermal dose is 240CEM43°C. It also showed that pulses with focal size smaller than or equal to 4 mm benefit the perfusion independence for the following quantities: the upper bound on the peak temperature, the treatment size, and the time/temperature for which 90% thermal dose is accumulated. Thus the conduction dominates the cooling process for each single pulse heated by the highly focused SFUS applicators when the pulses are properly isolated temporally. Results from this study further provide an estimation of the closest distance between two pulses and the time/temperature to re-activate the consecutive pulses. Thus the results can guide the researchers to design more efficient treatment protocol for multiple-pulse thermal therapies.

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