# US 2025/0384530 A1 · Iterative specularity factorization for image enhancement > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2025/0384530 A1 - Document ID: US20250384530A1 - Status: Published application - Kind: A1 - Application number: 19/236,243 - Filed: 2025-06-12 - Published: 2025-12-18 - Earliest claimed: 2024-06-12 - Assignees: International Institute of Information Technology, Hyderabad - Applicants: International Institute of Information Technology, Hyderabad - Inventors: P.J. Narayanan; Saurabh Saini - Web page: https://patentgrep.com/patent/US20250384530A1 ## CPC - G06T 5/60: using machine learning, e.g. neural networks - G06T 5/70: Denoising; Smoothing - G06T 5/92: based on global image properties - G06T 2207/20081: Training; Learning - G06T 2207/20084: Artificial neural networks [ANN] - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL ## Abstract Disclosed herein is a method for image enhancement. The method begins by receiving an input image, which is then decomposed into a plurality of K additive factors using a factorization network. The decomposition process involves iteratively performing an L1 optimization for K iterations, configured to approximate image specularity or highlights as matrix sparsity. A crucial aspect is the progressive relaxation of a sparsity constraint associated with the L1 optimization for each successive iteration, allowing for the extraction of increasingly less sparse additive factors. The factorization network utilizes learned parameters, such as thresholds, shrinkage values, or step sizes, for this optimization. Finally, an enhanced output image is generated by fusing the K additive factors through a fusion network. ## Claims ### Claim 1 A processor-implemented method for enhancing light in an image using a recursive factorization network and a fusion network, the method comprising: receiving, by the recursive factorization network, an input image as a first input from an image-capturing device; decomposing, via the recursive factorization network comprising a sequence of K iterative factorizations, the input image into a plurality of K additive factors, wherein the decomposing comprises: (i) performing an optimization process, at a first K iteration, to apply an unrolled L1 optimization on the first input over T inner iterations, to approximate estimate a first additive factor comprising an image specularity or highlights as matrix sparsity using learned parameters that are specific to the first K iteration; (ii) computing a second input by subtracting the first input from the first additive factor, wherein the second input corresponds to the input image with a reduced sparsity constraint; (iii) performing the optimization process, at a second K iteration, to apply the unrolled L1 optimization on the second input over T inner iterations, to estimate a second additive factor comprising an image specularity or highlights as matrix sparsity using learned parameters that are specific to the second K iteration; and (iv) progressively reducing the sparsity constraint associated with the input image for each consecutive iteration to enable the extraction of increasingly less sparse additive factors; processing the plurality of K additive factors using the fusion network to generate a plurality of enhancement maps configured to adjust pixel intensities in the input image; and generating an enhanced output image by applying the plurality of enhancement maps to the input image using a differentiable bilateral filtering layer for smoothness and artifact reduction. ### Claim 2 (depends on 1) The method of claim 1, wherein the recursive factorization network comprises a plurality of network layers that are trained by unrolling the steps of the optimization process into the network layers using hyperparameters. ### Claim 3 (depends on 1) The method of claim 1, wherein the recursive factorization network is trained using a factorization loss function to enable the decomposition of the first input into the plurality of K additive factors, wherein the factorization loss function constrains a ratio of signal energy in each kth additive factor, and the corresponding input for that kth factor iteration to a predetermined value vk, thereby gradually reducing the sparsity constraints to increase a number of pixels in a specular component of the plurality of K additive factors. ### Claim 4 (depends on 3) The method of claim 3, wherein the factorization loss function enables zero-reference training of the recursive factorization network. ### Claim 5 (depends on 1) The method of claim 1, wherein progressively reducing the sparsity constraint comprises adjusting the hyperparameter of the recursive factorization network that controls an amount of the sparsity in a solution of the unrolled L1 optimization for each of the K iterations. ### Claim 6 (depends on 1) The method of claim 1, wherein the fusion network is trained using at least one of color constancy loss, an exposure loss, or pixel-wise smoothing loss to enhance and denoise the plurality of K additive factors. ### Claim 7 (depends on 1) The method of claim 1, wherein the fusion network utilizes a task-dependent pre-existing network architecture adapted for a specific image enhancement task selected from the group consisting of low-light enhancement, deraining, dehazing, and deblurring. ### Claim 8 (depends on 1) The method of claim 1, wherein the learned parameters for each k iteration comprises at least one of threshold, shrinkage values and step size for each of the T inner iterations within the unrolled L1 optimization. ### Claim 9 A system for enhancing light in an image using a recursive factorization network and a fusion network, the system comprising: a processor; and a memory storing instructions that, when executed by the processor, configure the system to: receive, by the recursive factorization network, an input image as a first input from an image-capturing device; decompose, via the recursive factorization network comprising a sequence of K iterative factorizations, the input image into a plurality of K additive factors by: a. performing an optimization process, at a first K iteration, to apply an unrolled L1 optimization on the first input over T inner iterations, to estimate a first additive factor comprising an image specularity or highlights as matrix sparsity using learned parameters that are specific to the first K iteration; b. computing a second input by subtracting the first input from the first additive factor, wherein the second input corresponds to the input image with a reduced sparsity constraint; c. performing the optimization process, at a second K iteration, to apply the unrolled L1 optimization on the second input over T inner iterations, to estimate a second additive factor comprising an image specularity or highlights as matrix sparsity using learned parameters that are specific to the second K iteration; and d. progressively reducing the sparsity constraint associated with the input image for each consecutive iteration to enable the extraction of increasingly less sparse additive factors; process the plurality of K additive factors using the fusion network to generate a plurality of enhancement maps configured to adjust pixel intensities in the input image; and generate an enhanced output image by applying the plurality of enhancement maps to the input image using a differentiable bilateral filtering layer for smoothness and artifact reduction. ### Claim 10 (depends on 9) The system of claim 9, wherein the recursive factorization network comprises a plurality of network layers that are trained by unrolling the steps of the optimization process into the network layers using hyperparameters. ### Claim 11 (depends on 9) The system of claim 9, wherein the instructions further configure the recursive factorization network to be trainable using a factorization loss function to enable the decomposition of the first input into the plurality of K additive factors, wherein the factorization loss function constrains a ratio of signal energy in each kth additive factor and the corresponding input for that kth factor iteration to a predetermined value vk, thereby gradually reducing the sparsity constraints to increase a number of pixels in a specular component of the plurality of K additive factors. ### Claim 12 (depends on 11) The system of claim 11, wherein the factorization loss function enables zero-reference training of the recursive factorization network. ### Claim 13 (depends on 9) The system of claim 9, wherein the recursive factorization network is configured such that progressively reducing the sparsity constraint comprises adjusting the hyperparameter of the recursive factorization network that controls an amount of the sparsity in a solution of the unrolled L1 optimization for each of the K iterations. ### Claim 14 (depends on 9) The system of claim 9, wherein the fusion network is trained using at least one of color constancy loss, an exposure loss, or pixel-wise smoothing loss to enhance and denoise the plurality of K additive factors. ### Claim 15 (depends on 9) The system of claim 9, wherein the fusion network utilizes a task-dependent pre-existing network architecture adapted for a specific image enhancement task selected from the group consisting of low-light enhancement, deraining, dehazing, and deblurring. ### Claim 16 (depends on 9) The system of claim 9, wherein the learned parameters for each k iteration comprises at least one of threshold, shrinkage values and step size for each of the T inner iterations within the unrolled L1 optimization. ### Claim 17 (canceled)