EP-4741860-A1 - METHOD AND SYSTEM FOR CURRENT DENSITY MAPS RECONSTRUCTION BY JOINTLY OPTIMIZING MAGNETIC FIELD MAPS

Abstract

Embodiments herein provide a method and system for current density maps reconstruction by jointly optimizing x-direction, y-direction and z-direction magnetic field maps. Herein, the method of reconstruction of current image is leveraging state of the art iterative reconstruction techniques along with deep learning techniques. The quality of the current reconstruction depends on the signal to noise ratio (SNR) of the magnetic field observed. Since the noise model is difficult to characterize, a deep neural network is trained to learn the complex noise model from the data itself. To simulate the realistic scenarios, training data is created by introducing various kinds of noise that may appear in the system and collecting the training data pairs, i.e., pair of noisy and denoised x-direction and y- direction current density maps. The DNN is trained on this paired data to learn the noise model.

Inventors

• Reddy Kancham, Pavan Kumar
• Anand, Prabhat Sneh
• KUMAR, ACHANNA ANIL
• KHANDELWAL, Ankit
• CHANDRA, MARISWAMY GIRISH

Assignees

• Tata Consultancy Services Limited

Dates

Publication Date

20260513

Application Date

20251028

Claims (15)

1. A processor-implemented method (300) for current density maps reconstruction by jointly optimizing x-direction, y-direction and z-direction magnetic field maps comprising: detecting (302), via one or more hardware processors, a plurality of magnetic field maps along x-direction ( B x ) , y-direction ( B y ), and z-direction ( B z ) using a quantum sensing technique; representing (304), via the one or more hardware processors, the plurality of magnetic field maps into an energy function comprising the plurality of magnetic field maps along x-direction ( B x ) , y-direction ( B y ) and, z-direction ( B z ), a plurality of Green's functions, and a plurality of electric current density maps along x-direction ( J x ′ ) and y-direction ( J y ′ ); appending (306), via the one or more hardware processors, the energy function with one or more predefined additional regularization functions to generate a regularized energy function; and jointly optimizing (308), via the one or more hardware processors, the regularized energy function using a variable splitting technique to obtain a plurality of denoised electric current density maps along x-direction ( J x ) , and a plurality of denoised electric current density maps along y-direction ( J y ) .
2. The processor-implemented method (300) as claimed in claim 1, wherein jointly optimizing the regularized energy function using a variable splitting technique by: iteratively performing inversion mechanism on the plurality of magnetic field maps along x-direction ( B x ) and y-direction ( B y ), and z-direction ( B z ), to obtain a plurality of noisy electric current density maps along x-direction ( J x ′ ), and a plurality of noisy electric current density maps along y-direction ( J y ′ ); and jointly denoising the plurality of noisy electric current density maps along x-direction ( J x ′ ) and the plurality of noisy electric current density maps along y-direction ( J y ′ ), using a pretrained Deep Neural Network (DNN) denoising model.
3. The processor-implemented method (300) as claimed in claim 2, wherein the DNN denoising model is trained by: collecting a plurality of x-direction electric current density map pairs and a plurality of y-direction electric current density map pairs; and feeding the plurality of x-direction electric current density map pairs and the plurality of y-direction electric current density map pairs to the DNN denoising model to train the DNN denoising model.
4. The processor-implemented method (300) as claimed in claim 1, wherein the trained DNN denoising model upon receiving a new noisy electric current density map along x-direction ( J x ′ ) and a new noisy current density map along y-direction ( J y ′ ), predicts the denoised electric current density map along x-direction ( J x ) , and denoised electric current density map along y-direction ( J y ).
5. The processor-implemented method (300) as claimed in claim 1, wherein a x-direction electric current density map pair is comprising of a noisy electric current density map along x-direction ( J x ′ ) and a denoised electric current density map along x-direction ( J x ) .
6. The processor-implemented method (300) as claimed in claim 1, wherein a y-direction electric current density map pair is comprising of a noisy electric current density map along y-direction ( J y ′ ) and a denoised electric current density map along y-direction ( J y ) .
7. A system (100) current reconstruction by joint optimization x-direction and y-direction magnetic field comprising: a memory (110) storing instructions; one or more Input/Output (I/O) interfaces (104); and one or more hardware processors (108) coupled to the memory (110) via the one or more I/O interfaces (104), wherein the one or more hardware processors (108) are configured by the instructions to: detect a plurality of magnetic field maps along x-direction ( B x ), y-direction ( B y ), and z-direction ( B z ) using a quantum sensing technique; represent the plurality of magnetic field maps into an energy function comprising the plurality of magnetic field maps along x-direction ( B x ), y-direction ( B y ) and, z-direction ( B z ), a plurality of Green's functions, and a plurality of electric current density maps along x-direction ( J x ′ ) and y-direction ( J y ′ ); append the energy function with one or more additional regularization functions to generate a regularized energy function; and jointly optimize the regularized energy function using a variable splitting technique to obtain a plurality of denoised electric current density maps along x-direction ( J x ) , and a plurality of denoised electric current density maps along y-direction ( J y ) .
8. The system (100) as claimed in claim 7, wherein the one or more hardware processors are configured to jointly optimize the regularized energy function using the variable splitting technique by: iteratively performing inversion mechanism on the plurality of magnetic field maps along x-direction ( B x ) and y-direction ( B y ), and z-direction ( B z ), to obtain a plurality of noisy electric current density maps along x-direction ( J x ′ ), and a plurality of noisy electric current density maps along y-direction ( J y ′ ); and jointly denoising the plurality of noisy electric current density maps along x-direction ( J x ′ ) and the plurality of noisy electric current density maps along y-direction ( J y ′ ), using a pretrained Deep Neural Network (DNN) denoising model.
9. The system (100) as claimed in claim 8, wherein the DNN denoising model is trained by: collecting a plurality of x-direction electric current density map pairs and a plurality of y-direction electric current density map pairs; and feeding the plurality of x-direction electric current density map pairs and the plurality of y-direction electric current density map pairs to the DNN denoising model to train the DNN denoising model.
10. The system (100) as claimed in claim 7, wherein the trained DNN noise model upon receiving a new noisy electric current density map along x-direction ( J x ′ ) and a new noisy current density map along y-direction ( J y ′ ), predicts the denoised electric current density map along x-direction ( J x ) , and denoised electric current density map along y-direction ( J y ) .
11. The system (100) as claimed in claim 7, wherein a x-direction electric current density map pair of the plurality of x-direction electric current density map pairs is composed of a noisy electric current density map along x-direction ( J x ′ ) and a denoised electric current density map along x-direction ( J x ) .
12. The system (100) as claimed in claim 7, wherein a y-direction electric current density map pair of the plurality of y-direction electric current density map pairs is composed of the plurality of noisy electric current density map pair along y-direction ( J y ) and a denoised electric current density map pair along y-direction ( J y ) .
13. One or more non-transitory machine-readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors cause: detecting a plurality of magnetic field maps along x-direction ( B x ) , y-direction ( B y ), and z-direction ( B z ) using a quantum sensing technique; representing the plurality of magnetic field maps into an energy function comprising the plurality of magnetic field maps along x-direction ( B x ) , y-direction ( B y ) and, z-direction ( B z ), a plurality of Green's functions, and a plurality of electric current density maps along x-direction ( J x ′ ) and y-direction ( J y ′ ); appending the energy function with one or more additional regularization functions to generate a regularized energy function; and jointly optimizing the regularized energy function using a variable splitting technique to obtain a plurality of denoised electric current density maps along x-direction ( J x ) , and a plurality of denoised electric current density maps along y-direction ( J y ) .
14. The one or more non-transitory machine-readable information storage mediums as claimed in claim 13, wherein jointly optimizing the regularized energy function using a variable splitting technique by: iteratively performing inversion mechanism on the plurality of magnetic field maps along x-direction ( B x ) and y-direction ( B y ), and z-direction ( B z ), to obtain a plurality of noisy electric current density maps along x-direction ( J x ′ ), and a plurality of noisy electric current density maps along y-direction ( J y ′ ); and jointly denoising the plurality of noisy electric current density maps along x-direction ( J x ′ ) and the plurality of noisy electric current density maps along y-direction ( J y ′ ), using a pretrained Deep Neural Network (DNN) denoising model.
15. The one or more non-transitory machine-readable information storage mediums as claimed in claim 14, wherein the DNN denoising model is trained by: collecting a plurality of x-direction electric current density map pairs and a plurality of y-direction electric current density map pairs; and feeding the plurality of x-direction electric current density map pairs and the plurality of y-direction electric current density map pairs to the DNN denoising model to train the DNN denoising model.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS AND PRIORITY The present application claims priority to Indian application no. 202421085737 filed on November 7, 2024. TECHNICAL FIELD The disclosure herein generally relates to the field of current density maps reconstruction, and more particularly, a method and system for current density maps reconstruction by jointly optimizing x-direction, y-direction and z-direction magnetic field maps. BACKGROUND Quantum sensing with NV (nitrogen-vacancy) centers in diamond represents a groundbreaking advancement in precision measurement. NV centers are specific defects within the diamond lattice where a nitrogen atom replaces a carbon atom, creating a vacancy adjacent to it. These centers exhibit remarkable quantum properties, such as spin states that are highly sensitive to external magnetic and electric fields. By using the NV centers as quantum sensors, researchers can achieve unprecedented levels of accuracy in detecting magnetic fields, temperature variations, and even electric fields at the nanoscale. Once the magnetic fields are available, it is also possible to obtain the current density maps which is of great interest to the semiconductor industry as the current can be non-destructively imaged and in turn defects in semiconductor ICs can be detected. Existing methods either use z-direction magnetic field or use x- and y-direction fields separately and combine them later. Reconstruction using just z-field has some challenges in applying the prior as we deal with the integral of the signal. Where with x and y fields we directly deal with the signal, however treating them separately leads to artifacts. Also, the reconstruction of the current image under low Signal to Noise Ratio (SNR) conditions is challenging. SUMMARY Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems. For example, in one embodiment, a method for current density maps reconstruction by jointly optimizing x-direction, y-direction and z-direction magnetic field maps is provided. The processor-implemented method includes detecting a plurality of magnetic field maps along x-direction (Bx), y-direction (By), and z-direction (Bz) using a quantum sensing technique. Further, the processor-implemented method includes representing the plurality of magnetic field maps into an energy function comprising the plurality of magnetic field maps along x-direction (Bx), y-direction (By) and, z-direction (Bz), a plurality of Green's functions, and a plurality of electric current density maps along x-direction ( Jx′) and y-direction ( Jy′). Furthermore, the processor-implemented method includes appending the energy function with one or more predefined additional regularization functions to generate a regularized energy function. Finally, the processor-implemented method includes jointly optimizing the regularized energy function using a variable splitting technique to obtain a plurality of denoised electric current density maps along x-direction (Jx), and a plurality of denoised electric current density maps along y-direction (Jy). In another embodiment, a system for current density maps reconstruction by jointly optimizing x-direction, y-direction and z-direction magnetic field maps is provided. The system comprises a memory storing a plurality of instructions, one or more Input/Output (I/O) interfaces, and one or more hardware processors coupled to the memory via the one or more I/O interfaces. The one or more hardware processors are configured by the instructions to detect a plurality of magnetic field maps along x-direction (Bx), y-direction (By), and z-direction (Bz) using a quantum sensing technique. Further, the one or more hardware processors are configured by the instructions to represent the plurality of magnetic field maps into an energy function comprising the plurality of magnetic field maps along x-direction (Bx), y-direction (By) and, z-direction (Bz), a plurality of Green's functions, and a plurality of electric current density maps along x-direction ( Jx′) and y-direction ( Jy′). The energy function is appended with one or more predefined additional regularization functions to generate a regularized energy function. Finally, the one or more hardware processors are configured by the instructions to jointly optimize the regularized energy function using a variable splitting technique to obtain a plurality of denoised electric current density maps along x-direction (Jx), and a plurality of denoised electric current density maps along y-direction (Jy). In yet another aspect, there are provided one or more non-transitory machine-readable information storage mediums comprising one or more instructions, which when executed by one or more hardware processors causes a method for a current density maps reconstruction by jointly optimizing x-direction, y-direction and z-directio