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1.
Chem Sci ; 15(28): 10969-10979, 2024 Jul 17.
Article in English | MEDLINE | ID: mdl-39027299

ABSTRACT

Phototherapy has garnered considerable interest for its potential to revolutionize conventional cancer treatment. Organic materials with near-infrared II (NIR-II, 1000-1700 nm) fluorescence and photothermal effects are key for precise tumor diagnosis and treatment, yet optimizing their output for higher resolution and reduced photodamage remains a challenge. Herein, a multifunctional NIR-II photosensitizer (LSC) has been developed using the aggregation-induced emission (AIE) technology. The utilization of thieno[3,2-b]thiophene as an electron-rich and bulky donor/acceptor bridge has allowed for the elongation of conjugation length and distortion of the AIE main chain. This strategic modification effectively enhances the electron push-pull effect, endowing the LSC with a Stokes shift of over 400 nm and AIE characteristics. We have successfully built-up stable nanoparticles called FA-LSC NPs using a nano-precipitation method. These nanoparticles exhibit high NIR-II fluorescent brightness (ε × QY = 1064 M-1 cm-1) and photothermal conversion efficiency (41%). Furthermore, the biocompatible FA-LSC NPs demonstrate effective tumor accumulation and exceptional photothermal therapeutic efficacy both in vitro and in vivo. These nanoparticles were applied to fluorescence-photothermal dual-mode imaging-guided photothermal ablation in a HeLa tumor xenograft mouse model, resulting in favorable photothermal clearance outcomes.

2.
Eur J Med Chem ; 275: 116581, 2024 Sep 05.
Article in English | MEDLINE | ID: mdl-38870831

ABSTRACT

Nucleotide-binding oligomerization domain-like receptor pyrin domain containing 3 (NLRP3) constitutes an essential inflammasome sensor protein, pivotal in the orchestration of innate immunity. Given its paramount role, NLRP3 has recently emerged as an enticing therapeutic target for disorders associated with inflammation. In this study, we embarked on the design and synthesis of two series of compounds, endowed with the capacity to induce NLRP3 degradation via autophagy-tethering compounds (ATTECs)-an innovative targeted protein degradation technology. Notably, MC-ND-18 emerged as the most potent agent for effectuating NLRP3 degradation through autophagic mechanisms and concurrently exhibited marked anti-inflammatory efficacy in mice model of dextran sulfate sodium (DSS)-induced colitis. Consequently, we have successfully developed a pioneering NLRP3 protein degrader, offering a novel therapeutic avenue for ameliorating NLRP3-associated pathologies.


Subject(s)
Autophagy , Dextran Sulfate , NLR Family, Pyrin Domain-Containing 3 Protein , NLR Family, Pyrin Domain-Containing 3 Protein/metabolism , NLR Family, Pyrin Domain-Containing 3 Protein/antagonists & inhibitors , Animals , Autophagy/drug effects , Mice , Humans , Molecular Structure , Structure-Activity Relationship , Inflammatory Bowel Diseases/drug therapy , Inflammatory Bowel Diseases/metabolism , Immunotherapy , Drug Discovery , Dose-Response Relationship, Drug , Mice, Inbred C57BL , Colitis/drug therapy , Colitis/chemically induced , Colitis/metabolism , Proteolysis/drug effects , Anti-Inflammatory Agents/pharmacology , Anti-Inflammatory Agents/chemistry , Anti-Inflammatory Agents/chemical synthesis
3.
Anal Chem ; 96(23): 9737-9743, 2024 Jun 11.
Article in English | MEDLINE | ID: mdl-38825763

ABSTRACT

Various signal molecules mediate complex physiological processes collectively in the Golgi. However, most currently accessible probes are questionable in illuminating the functions of these reactive species in Golgi because of the inability to irradiate these probes only at the desired Golgi location, which compromises specificity and accuracy. In this study, we rationally designed the first photocontrollable and Golgi-targeted fluorescent probe to in situ visualize the Golgi alkaline phosphatase (ALP). The designed probe with natural yellow fluorescence can provide access into Golgi and monitor the exact timing of accumulation in Golgi. On-demand photoactivation at only the desired Golgi location affords a significant emission response to ALP with illuminating red fluorescence at 710 nm. Through the photocontrollable fluorescence responsiveness to ALP, precise spatiotemporal recognition of Golgi ALP fluctuations is successfully performed. With this probe, for the first time, we revealed the Golgi ALP levels during cisplatin-induced acute kidney injury (AKI), which will further facilitate and complement the comprehensive exploration of ALP kinetics during physiological and pathological processes.


Subject(s)
Alkaline Phosphatase , Fluorescent Dyes , Golgi Apparatus , Golgi Apparatus/metabolism , Alkaline Phosphatase/metabolism , Humans , Animals , Fluorescent Dyes/chemistry , HeLa Cells , Mice , Cisplatin/pharmacology
4.
J Med Chem ; 67(9): 7431-7442, 2024 May 09.
Article in English | MEDLINE | ID: mdl-38664896

ABSTRACT

Since hydrogen sulfide (H2S) is an important endogenous gaseous mediator, therapeutic manipulation of H2S is promising for anticancer treatment. In this work, we develop a novel theranostic nanoplatform with H2S-specific and photocontrolled synergistic activation for imaging-guided H2S depletion and downregulation along with promoted photothermal therapy. Such a nanoplatform is fabricated by integration of a H2S-responsive molecule probe that can generate a cystathionine-ß-synthase (CBS) inhibitor AOAA and a photothermal transducer into an NIR-light-responsive container. Our nanoplatform can turn on NIR fluorescence specifically in H2S-rich cancers, guiding further laser irradiation. Furthermore, prominent conversion of photoenergy into heat guarantees special container melting with controllable AOAA release for H2S-level downregulation. This smart regulation of the endogenous H2S level amplifies the PTT therapeutic effect, successfully suppressing colorectal tumor in living mice under NIR fluorescence imaging guidance. Thus, we believe that this nanoplatform may provide a powerful tool toward H2S-concerned cancer treatment with an optimized diagnostic and therapeutic effect.


Subject(s)
Colorectal Neoplasms , Down-Regulation , Hydrogen Sulfide , Photothermal Therapy , Hydrogen Sulfide/metabolism , Hydrogen Sulfide/chemistry , Animals , Photothermal Therapy/methods , Colorectal Neoplasms/drug therapy , Colorectal Neoplasms/metabolism , Colorectal Neoplasms/therapy , Colorectal Neoplasms/pathology , Humans , Mice , Down-Regulation/drug effects , Cystathionine beta-Synthase/metabolism , Cystathionine beta-Synthase/antagonists & inhibitors , Optical Imaging , Antineoplastic Agents/pharmacology , Antineoplastic Agents/chemistry , Antineoplastic Agents/therapeutic use , Mice, Inbred BALB C , Mice, Nude , Nanoparticles/chemistry , Infrared Rays , Cell Line, Tumor , Theranostic Nanomedicine/methods
5.
J Opt Soc Am A Opt Image Sci Vis ; 41(3): A32-A39, 2024 Mar 01.
Article in English | MEDLINE | ID: mdl-38437421

ABSTRACT

A computer-generated hologram (CGH) is a technique that generates an object light field by superimposing elementary holograms. Unlike traditional holography, this technique does not require the generation of an additional reference light to interfere with the calculated object light field. Texture mapping is a method that enhances the realism of 3D scenes. A fast method is presented that allows users to render holograms of 3D scenes consisting of triangular meshes with texture mapping. All calculations are performed with analytical expressions to ensure that the holograms generated by this method are fast and can reconstruct three-dimensional scenes with high quality. Using this method, a hologram of a three-dimensional scene consisting of thousands of triangles is generated. Our algorithm generates the same reconstruction results as those of Kim et al. [Appl. Opt.47, D117 (2008)APOPAI0003-693510.1364/AO.47.00D117], but significantly reduces the computation time (the computation time of our algorithm is only one-third of that of Kim et al.'s algorithm). The results show that the proposed method is computationally efficient as compared to a previous work. The proposed method is verified by simulations and optical experiments.

6.
J Mater Chem B ; 12(9): 2304-2312, 2024 Feb 28.
Article in English | MEDLINE | ID: mdl-38348949

ABSTRACT

Nitric oxide (NO), a ubiquitous gaseous transmitter in living systems, is closely associated with physiopathological processes in the endoplasmic reticulum and lysosomes. This free radical gas is very widely but very heterogeneously distributed in the biological microenvironment, which poses a great challenge to specifically detect its localized levels in certain subcellular regions. In this study, we proposed six subcellular targeting probes by rational molecular engineering and selected two probes with optimal performance for the precise spatiotemporal identification of endoplasmic reticulum (ER) and lysosomal NO fluctuations. The probes could rapidly undergo a N-nitrosation reaction with NO at a riveted subcellular location, blocking the initial photoinduced electron transfer (PET) process and generating bright fluorescence for precise mapping of NO in the ER and lysosomes. The screened probes have ultra-sensitive reactivity and ultra-low detection limits for NO, realizing the precise depiction of exogenous and endogenous NO in the corresponding subcellular area. Fluctuations in the subcellular levels of NO during inflammation were also successfully mapped by the probes. Our work will contribute to the accurate study of the physiological and pathological consequences of subcellular NO in various biological events.


Subject(s)
Fluorescent Dyes , Nitric Oxide , Lysosomes , Endoplasmic Reticulum , Gases
7.
Anal Chem ; 96(3): 1259-1267, 2024 01 23.
Article in English | MEDLINE | ID: mdl-38206997

ABSTRACT

The increasing understanding of the intricate relationship between two crucial gasotransmitters nitric oxide (NO) and hydrogen sulfide (H2S) in biological actions has generated significant interest. However, comprehensive monitoring of the dynamic fluctuations of endogenous NO and H2S remains a challenge. In this study, we have designed an innovative aggregation-induced reporter SAB-NH-SC with enhanced responsiveness to H2S for visualizing the fluctuations of intracellular NO and H2S. This probe leverages the hydrophilic properties of the pyridinium salt derivative, which can rapidly self-assemble into positively charged nanoparticles under physiological conditions, avoiding the introduction of organic solvents or tedious preparations. Notably, the reporter can repeatedly cycle S-nitrosation and SNO-transnitrosation reactions when successively treated with NO and H2S. Consequently, fluorescence alternation at 751 (H2S) and 639 nm (NO) facilitates the dynamic visualization of the alternating presence of H2S and NO within cells. This dynamic and reversible probe holds immense potential for unraveling the intricate interactions between NO and H2S in a complex network of biological applications.


Subject(s)
Gasotransmitters , Hydrogen Sulfide , Nanoparticles , Nitric Oxide
8.
J Med Chem ; 67(1): 433-449, 2024 01 11.
Article in English | MEDLINE | ID: mdl-38112492

ABSTRACT

Proprotein convertase subtilisin/kexin type-9 (PCSK9), a secreted protein that is synthesized and spontaneously cleaved in the endoplasmic reticulum, has become a hot lipid-lowering target chased by pharmaceutical companies in recent years. Autophagosome-tethering compounds (ATTECs) represent a new strategy to degrade targeted biomolecules. Here, we designed and synthesized PCSK9·ATTECs that are capable of lowering PCSK9 levels via autophagy in vivo, providing the first report of the degradation of a secreted protein by ATTECs. OY3, one of the PCSK9·ATTECs synthesized, shows greater potency to reduce plasma low-density lipoprotein cholesterol (LDL-C) levels and improve atherosclerosis symptoms than treatment with the same dose of simvastatin. OY3 also significantly reduces the high expression of PCSK9 caused by simvastatin administration in atherosclerosis model mice and subsequently increases the level of low-density lipoprotein receptor, promoting simvastatin to clear plasma LDL-C and alleviate atherosclerosis symptoms. Thus, we developed a new candidate compound to treat atherosclerosis that could also promote statin therapy.


Subject(s)
Atherosclerosis , Proprotein Convertase 9 , Mice , Animals , Proprotein Convertase 9/metabolism , Cholesterol, LDL/metabolism , Cholesterol, LDL/therapeutic use , Simvastatin/pharmacology , Simvastatin/therapeutic use , Receptors, LDL/metabolism , Atherosclerosis/drug therapy , Atherosclerosis/metabolism , Autophagy
9.
Small ; 20(22): e2309529, 2024 May.
Article in English | MEDLINE | ID: mdl-38100303

ABSTRACT

Carbon monoxide shows great therapeutic potential in anti-cancer. In particular, the construction of multifunctional CO delivery systems can promote the precise delivery of CO and achieve ideal therapeutic effects, but there are still great challenges in design. In this work, a RSS and ROS sequentially activated CO delivery system is developed for boosting NIR imaging-guided on-demand photodynamic therapy. This designed system is composed of a CO releaser (BOD-CO) and a photosensitizer (BOD-I). BOD-CO can be specifically activated by hydrogen sulfide with simultaneous release of CO donor and NIR fluorescence that can identify H2S-rich tumors and guide light therapy, also depleting H2S in the process. Moreover, BOD-I generates 1O2 under long-wavelength light irradiation, enabling both PDT and precise local release of CO via a photooxidation mechanism. Such sequential activation of CO release by RSS and ROS ensured the safety and controllability of CO delivery, and effectively avoided leakage during delivery. Importantly, cytotoxicity and in vivo studies reveal that the release of CO combined with the depletion of endogenous H2S amplified PDT, achieving ideal anticancer results. It is believed that such theranostic nanoplatform can provide a novel strategy for the precise CO delivery and combined therapy involved in gas therapy and PDT.


Subject(s)
Carbon Monoxide , Photochemotherapy , Reactive Oxygen Species , Photochemotherapy/methods , Carbon Monoxide/chemistry , Reactive Oxygen Species/metabolism , Humans , Animals , Cell Line, Tumor , Photosensitizing Agents/chemistry , Photosensitizing Agents/pharmacology , Mice , Infrared Rays , Hydrogen Sulfide/chemistry
10.
ACS Nano ; 17(21): 22060-22070, 2023 11 14.
Article in English | MEDLINE | ID: mdl-37889140

ABSTRACT

Understanding biological events associated with H2Sn rather than mediated by H2S is of great significance but remains to be solved due to a lack of high-integrity imaging tools. In this study, we report a chemoselective probe for H2Sn over H2S through the molecular engineering of luminogens. Based on our search for H2Sn-activatable probes with high selectivity, we fabricate water-soluble and biocompatible nanoprobes. Such a designed nanoprobe shows rare aggregation-induced dual-color fluorescence responses to H2Sn, lighting up bright emissions at 588 and 750 nm, respectively. By use of this activatable dual-color fluorescence, high-integrity identification of intracellular H2Sn was successfully realized. Thus, our approach to H2Sn-activated multicolor fluorescent probes could provide valuable insight into interrogating H2Sn-mediated biological events.


Subject(s)
Hydrogen Sulfide , Hydrogen , Sulfides , Fluorescent Dyes , Optical Imaging/methods
11.
Anal Chem ; 95(38): 14288-14296, 2023 09 26.
Article in English | MEDLINE | ID: mdl-37697825

ABSTRACT

Various signal molecules participate in complex biological processes in mitochondria. However, most currently available probes have problems in elucidating the functions of these active species in mitochondria due to the inability to light up these probes exclusively at the desired mitochondrial location, thereby compromising the specificity and accuracy. In this study, we present an on-demand photoactivation approach to the molecular design of optimized probes for precise spatiotemporal identification of mitochondrial H2S fluctuations. The designed probe with native yellow fluorescence can monitor the process into mitochondria but maintains nonfluorescent response to H2S during cellular delivery, providing the accurate timing of accumulation in mitochondria. On-demand photoactivation exclusively at the desired mitochondrial location affords a significant aggregation-enhanced and emissive response to H2S with lighting up red fluorescence at 690 nm, which is the only way to get such an emissive phenomenon and greatly improves the specificity and accuracy of targeting mitochondrial H2S. By using this photocontrolled fluorescence responsiveness to H2S, precise spatiotemporal identification of mitochondrial H2S fluctuations is successfully performed. Our work could facilitate advances toward interrogating the physiological and pathological consequences of mitochondrial H2S in various biological events.


Subject(s)
Hydrogen Sulfide , Humans , Fluorescent Dyes , HeLa Cells , Mitochondria , Microscopy, Fluorescence
12.
Opt Express ; 31(15): 24537-24554, 2023 Jul 17.
Article in English | MEDLINE | ID: mdl-37475278

ABSTRACT

We have developed a full analytical method with texture mapping for polygon-based computer-generated holography. A parallel planar projection mapping for holographic rendering along with affine transformation and self-similar segmentation is derived. Based on this method, we further propose a parallelogram-approximation to reduce the number of polygons used in the polygon-based technique. We demonstrate that the overall method can reduce the computational effort by 50% as compared to an existing method without sacrificing the reconstruction quality based on high precision rendering of complex textures. Numerical and optical reconstructions have shown the effectiveness of the overall scheme.

13.
Org Biomol Chem ; 21(29): 5919-5923, 2023 07 26.
Article in English | MEDLINE | ID: mdl-37435862

ABSTRACT

An H2O2-activated, endoplasmic reticulum-targeted theranostic probe was developed. This designed probe could be activated by H2O2, resulting in increased NIR fluorescence and photothermal signals, thus achieving specific recognition of H2O2 and further photothermal therapy in the endoplasmic reticulum of H2O2-overexpressing cancer cells.


Subject(s)
Nanoparticles , Neoplasms , Humans , Photothermal Therapy , Phototherapy/methods , Hydrogen Peroxide , Theranostic Nanomedicine/methods , Endoplasmic Reticulum , Cell Line, Tumor
14.
Article in English | MEDLINE | ID: mdl-37262120

ABSTRACT

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG. To augment reader accessibility, a dedicated IMG project page is available at https://github.com/xzb030/IMG_Survey.

15.
Chem Sci ; 13(33): 9525-9530, 2022 Aug 24.
Article in English | MEDLINE | ID: mdl-36128038

ABSTRACT

Photothermal agents (PTAs) with minimized side effects are critical for transforming cancer photothermal therapy (PTT) into clinical applications. However, most currently available PTAs lack true selective activation to reduce side effects because of heavy spectral overlap between photothermal agents and their corresponding products. This study reports the construction of activatable PTAs with target-initiated large spectral separation for highly effective reduction of side effects. Such designed probes involve two H2O2-activatable PTAs, aza-BOD-B1 (single activatable site) and aza-BOD-B2 (multiple activatable site). After interacting with H2O2, aza-BOD-B1 only displays a mild absorption redshift (60 nm) from 750 nm to 810 nm with serious spectral overlap, resulting in a mild photothermal effect on normal tissues upon 808 nm light irradiation. In contrast, aza-BOD-B2 displays a large absorption spectral separation (150 nm) from 660 nm to 810 nm, achieving true selective activation to minimize side effects during PTT of cancer. Besides, in vitro and in vivo investigations demonstrated that aza-BOD-B2 can specifically induce photothermal ablation of cancer cells and tumors while leaving normal sites undamaged, whereas aza-BOD-B1 exhibits undesirable side effects on normal cells. Our study provides a practical solution to the problem of undesired side effects of phototherapy, an advance in precision medicine.

16.
Bioorg Med Chem Lett ; 68: 128762, 2022 07 15.
Article in English | MEDLINE | ID: mdl-35490954

ABSTRACT

γ-glutamyl transpeptidase (GGT) is a kind of cell-surface enzyme that is overexpressed in many cancer cells. It is of great significance to develop an ideal tool for the diagnosis of GGT-rich cancer cells. Here, we reported a simple-structured but effective imaging probe for the detection of GGT activity. In the presence of GGT, the γ-glutamyl linkage could be cleaved specifically to produce amino-substituted product, resulting in significant fluorescence enhancement at 578 nm. Moreover, we successfully employed the probe to monitor GGT activity in HepG2 cells. We envisaged that such a simple but effective imaging tool could improve the practical applications for bioimaging.


Subject(s)
Fluorescent Dyes , gamma-Glutamyltransferase , Fluorescence , Hep G2 Cells , Humans , Water
17.
Appl Opt ; 61(5): B363-B374, 2022 Feb 10.
Article in English | MEDLINE | ID: mdl-35201160

ABSTRACT

In this review paper, we first provide comprehensive tutorials on two classical methods of polygon-based computer-generated holography: the traditional method (also called the fast-Fourier-transform-based method) and the analytical method. Indeed, other modern polygon-based methods build on the idea of the two methods. We will then present some selective methods with recent developments and progress and compare their computational reconstructions in terms of calculation speed and image quality, among other things. Finally, we discuss and propose a fast analytical method called the fast 3D affine transformation method, and based on the method, we present a numerical reconstruction of a computer-generated hologram (CGH) of a 3D surface consisting of 49,272 processed polygons of the face of a real person without the use of graphic processing units; to the best of our knowledge, this represents a state-of-the-art numerical result in polygon-based computed-generated holography. Finally, we also show optical reconstructions of such a CGH and another CGH of the Stanford bunny of 59,996 polygons with 31,724 processed polygons after back-face culling. We hope that this paper will bring out some of the essence of polygon-based computer-generated holography and provide some insights for future research.

18.
Bioorg Med Chem Lett ; 59: 128544, 2022 03 01.
Article in English | MEDLINE | ID: mdl-35031453

ABSTRACT

Nitric oxide (NO) is an essential cellular messenger molecule involved in various physiological and pathological processes. Thus, monitoring the dynamic presence of endogenous NO in living cells is of great significance. In this paper, we developed an activatable fluorescent nanoprobe BOD-NH-NP for endogenous NO detection. In the probe BOD-NH-NP, the fast responding reaction site towards NO, incorporating a BODIPY fluorescent dye with good optical features, enables the probe to be applied for the detection of endogenous NO via the eNOS enzymatic pathway in living cells and screening nitric oxide synthases (NOSs) inhibitors and agonists.


Subject(s)
Fluorescent Dyes/chemistry , Nitric Oxide Synthase Type III/metabolism , Nitric Oxide/analysis , Animals , Cell Line , Molecular Structure , Nitric Oxide/metabolism , Optical Imaging , Rats
19.
Proc Int Conf Image Proc ; 2022: 1191-1195, 2022 Oct.
Article in English | MEDLINE | ID: mdl-37974614

ABSTRACT

Demand for efficient image transmission and storage is increasing rapidly because of the continuing growth of multimedia technology and VR and AR applications. In this paper, we proposed an image compression method based on the recognition of importance of regions in images. As not all the information in an image is equally useful, we can identify important regions in an image for high fidelity compression and accept a comparatively more lossy compression about less important regions of the image. First, we segment images to two parts, namely, foreground and background, where the foreground represents the more important component and the background is of less importance. Second, we apply optimal mass transportation mapping in a GAN (generative adversarial network) framework to both the foreground and background to magnify the foreground and shrink the background while keeping the shape and total image area unchanged. As a result, in the processed image, the ratio of foreground to background is larger than the corrresponding ratio in the original image. This ratio is controllable in our process, giving users the ability to control the degree of compression. The GAN-processed image is then used for compression. To restore the image, we apply a GAN model to the compressed image and recover the ratio of foreground and background using an optimal mass transportation map. Test results show that our method is highly effective in reconstructing detail of important components in compressed images while achieving a high compression ratio.

20.
Proc AAAI Conf Artif Intell ; 36(9): 10119-10128, 2022 Jun.
Article in English | MEDLINE | ID: mdl-37974660

ABSTRACT

Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete OT for large scale problems with adequate accuracy and efficiency is highly challenging. Recently, methods based on the Sinkhorn algorithm add an entropy regularizer to the prime problem and obtain a trade off between efficiency and accuracy. In this paper, we propose a novel algorithm based on Nesterov's smoothing technique to further improve the efficiency and accuracy in computing OT. Basically, the non-smooth c-transform of the Kantorovich potential is approximated by the smooth Log-Sum-Exp function, which smooths the original non-smooth Kantorovich dual functional. The smooth Kantorovich functional can be efficiently optimized by a fast proximal gradient method, the fast iterative shrinkage thresholding algorithm (FISTA). Theoretically, the computational complexity of the proposed method is given by O(n52logn∕ϵ), which is lower than current estimation of the Sinkhorn algorithm. Experimentally, compared with the Sinkhorn algorithm, our results demonstrate that the proposed method achieves faster convergence and better accuracy with the same parameter.

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