Recent multimodal foundation models are primarily trained on English or high resource European language data, which limits their applicability to other medium and low-resource languages, such as the Indian languages. To address this limitation, we introduce Chitrarth (Chitra: Image; Artha: Meaning), an inclusive Vision-Language Model (VLM), specifically targeting the rich linguistic diversity and visual reasoning across 10 prominent Indian languages. Our model effectively integrates a state-of-the-art (SOTA) multilingual Large Language Model (LLM) with a vision module, primarily trained on multilingual image-text data. Furthermore, we also introduce BharatBench, a comprehensive framework for evaluating VLMs across various low resource languages, ultimately contributing to more diverse and effective AI systems. Our model presents SOTA results for benchmarks across Indian languages while retaining its efficiency in English. Through our research, we aim to set new benchmarks in multilingual-multimodal capabilities, offering substantial improvements over existing models and establishing a foundation for facilitating future advancements in this arena.

Sparse coding methods are iterative and typically rely on proximal gradient methods. While the commonly used sparsity promoting penalty is the ℓ1norm, alternatives such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) penalty have also been employed to obtain superior results. Combining various penalties to achieve robust sparse recovery is possible, but the challenge lies in parameter tuning. Given the connection between deep networks and unrolling of iterative algorithms, it is possible to unify the unfolded networks arising from different formulations. We propose an ensemble of proximal networks for sparse recovery, where the ensemble weights are learnt in a data-driven fashion. We found that the proposed network performs superior to or on par with the individual networks in the ensemble for synthetic data under various noise levels and sparsity conditions. We demonstrate an application to image denoising based on the convolutional sparse coding formulation.

-norm, respectively. Convex approximations are known to result in biased estimates, to overcome which, nonconvex regularizers such as weighted nuclear-norm minimization and weighted Schatten p-norm minimization have been proposed. However, works employing these regularizers have used heuristic weight-selection strategies. We propose weighted minimax-concave penalty (WMCP) as the nonconvex regularizer and show that it admits an equivalent representation that enables weight adaptation. Similarly, an equivalent representation to the weighted matrix gamma norm (WMGN) enables weight adaptation for the low-rank part. The optimization algorithms are based on the alternating direction method of multipliers technique. We show that the optimization frameworks relying on the two penalties, WMCP and WMGN, coupled with a novel iterative weight update strategy, result in accurate low-rank plus sparse matrix decomposition. The algorithms are also shown to satisfy descent properties and convergence guarantees. On the applications front, we consider the problem of foreground-background separation in video sequences. Simulation experiments and validations on standard datasets, namely, I2R, CDnet 2012, and BMC 2012 show that the proposed techniques outperform the benchmark techniques.

We address the problem of recovering signals from compressed measurements based on generative priors. Recently, generative-model based compressive sensing (GMCS) methods have shown superior performance over traditional compressive sensing (CS) techniques in recovering signals from fewer measurements. However, it is possible to further improve the performance of GMCS by introducing controlled sparsity in the latent-space. We propose a proximal meta-learning (PML) algorithm to enforce sparsity in the latent-space while training the generator. Enforcing sparsity naturally leads to a union-of-submanifolds model in the solution space. The overall framework is named as sparsity driven latent space sampling (SDLSS). In addition, we derive the sample complexity bounds for the proposed model. Furthermore, we demonstrate the efficacy of the proposed framework over the state-of-the-art techniques with application to CS on standard datasets such as MNIST and CIFAR-10. In particular, we evaluate the performance of the proposed method as a function of the number of measurements and sparsity factor in the latent space using standard objective measures. Our findings show that the sparsity driven latent space sampling approach improves the accuracy and aids in faster recovery of the signal in GMCS.

We address the problem of efficient convolutional sparse coding (CSC) and develop a non-convex-penalty-regularized CSC formulation, namely, minimax-concave CSC (MC2SC). MC2SC leads to an optimal sparse representation than the standard ℓ1-penalty based approach. In addition, suitable convergence guarantees can also be provided for MC2SC. We propose a convolutional iterative firm-thresholding algorithm (CIFTA) building on our previously proposed IFTA, and its deep-unfolded version, namely, convolutional-FirmNet (ConFirmNet). As an application, we develop the ConFirmNet based sparse autoencoder (ConFirmNet-SAE) for learning an application-specific convolutional dictionary, the applications being image denoising and inpainting. Further, we also show that training ConFirmNet-SAE with the Huber loss imparts robustness to outliers. It also turns out that ConFirmNet-SAE is robust to mismatch between training and test noise conditions than convolutional learned iterative soft-thresholding algorithm (LISTA).

We present a new sparsity based technique for interferometric phase estimation. We consider complex extensions of non-convex regularizers such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation penalty (SCAD) for sparse recovery. We solve the problem of interferometric phase estimation based on complex-domain dictionary learning. We develop an algorithm, namely, improved sparse interferometric phase estimation (iSpInPhase) based on alternating direction method of multipliers (ADMM) and Wirtinger calculus for solving the optimization problem. Wiritinger calculus is employed because the cost functions are nonholomorphic. We evaluate the performance of iSpInPhase on synthetic data, namely, truncated Gaussian elevation and also on mountain terrain data, namely, Long's peak, for different noise levels. Performance comparisons show that iSpInPhase outperforms the state-of-the-art techniques in terms of standard performance assessment measures.

Sparse recovery via composite regularization is an interesting approach proposed recently in the literature. One could design nonconvex regularizers through a convex combination of sparsity-promoting penalties with known proximal operators. We develop a new algorithm, namely, convolutional proximal-averaged thresholding algorithm (C-PATA) for composite-regularized convolutional sparse coding (CR-CSC) based on the recently proposed idea of proximal averaging. We develop an autoencoder structure based on the deep-unfolding of C-PATA iterations into neural network layers, which results in the composite-regularized neural network (CoRNet) architecture. The convolutional learned iterative soft-thresholding algorithm becomes a special case of CoRNet. We demonstrate the efficacy of CoRNet considering applications to image denoising and inpainting, and compare the performance with state-of-the-art techniques such as BM3D, convolutional LISTA, and fast and flexible convolutional sparse coding (FFCSC).

We present a new method for fast magnetic resonance image (MRI) reconstruction in the complex-domain under tight frames. We propose a generalized problem formulation that allows for different weight-update strategies for iteratively reweighted ℓ1-minimization under tight frames. Further, we impose sufficient conditions on the function of the weights that leads to the reweighting strategy, which follows the interpretation originally given by Candès et al, but is more efficient than theirs. Since the objective function in complex-domain compressive sensing MRI (CS-MRI) reconstruction problem is nonholomorphic, we resort to Wirtinger calculus for deriving the update strategies. We develop an algorithm called generalized iteratively reweighted soft-thresholding algorithm (GIRSTA) and its fast variant, namely, generalized fast iteratively reweighted soft-thresholding algorithm (GFIRSTA). We provide convergence guarantees for GIRSTA and empirical convergence results for GFIRSTA. Our experiments show a remarkable performance of the proposed algorithms for complex-domain CS-MRI reconstruction considering both random sampling and radial sampling strategies. GFIRSTA outperforms state-of-the-art techniques in terms of peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM).

The analysis-sparse model has been shown to be efficient as compared to the synthesis-sparse model when the sparsifying transform is redundant particularly for image restoration applications. We pose the image deblurring problem as an optimization problem based on the analysis-sparse model considering the sparsifying basis to be a tight frame, more specifically, the shift-invariant discrete wavelet transform (SIDWT). We propose two algorithms, namely, projected improved fast iterative soft-thresholding algorithm (piFISTA) and projected improved fast iterative soft-thresholding algorithm beyond Nesterov's momentum (piFISTA-BN). The proposed algorithms are the analysis counterparts of the improved fast iterative soft-thresholding algorithm (iFISTA) and improved fast iterative soft-thresholding algorithm beyond Nesterov's momentum (iFISTA-BN), respectively, both of which consider the synthesis-sparse model. We demonstrate that piFISTA and piFISTA-BN significantly outperform FISTA, pFISTA, iFISTA, and iFISTA-BN considering standard objective metrics such as peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). Further, we demonstrate empirically that the proposed algorithms converge faster than the state-of-the-art techniques.

In ultrasound imaging, one typically employs delay-and-sum (DAS) beamformers for image reconstruction. An apodization window is used to suppress the side-lobes of an array beam pattern. The application of an apodization window to suppress the side-lobes widens the main-lobe width. We consider a statistical beamformer and present two variants. The signal of interest is modeled as a Laplacian-distributed random variable and additive interference components as Gaussian distributed. The resultant LASSO formulation is known to suffer from underestimation of large signal amplitudes due to the ℓ1-norm regularization. In the first variant, we reformulate the LASSO problem with a minimax-concave penalty (called Sparsity AMplified (SAM)) to contain the bias, thereby enhancing the beamformed image. A closed-form pointwise estimator is obtained for the optimization problem. In the second variant, we propose Sparsity AMplified Iteratively-Reweighted (SAMIR) beamforming algorithm, which leverages the properties of an apodization function. In SAMIR beamforming, we jointly optimize the cost over the signal of interest and the extrinsic apodization weights. This beamformer results in high-resolution ultrasound images, especially in the lateral direction. The proposed methods are compared with the standard DAS and a recently proposed statistically-modeled beamformer, iMAP, for a different number of plane-wave insonifications.

Recovering a sparse signal from a noisy linear measurement is an important problem in signal processing. Typically, one employs greedy pursuit techniques such as OMP, CoSaMP to solve an ℓ0regularization problem. For large-scale problems, iterative shrinkage techniques such as ISTA, FISTA, AMP-ℓ1have been introduced. The underlying formulation in the iterative algorithms is a LASSO problem with an ℓ1-penalty. It is known in the literature that an ℓ1-penalty in LASSO suffers from underestimation of large signal amplitudes. Also, the iterative shrinkage-based approaches such as ISTA typically have only one free parameter to trade-off between noise variance and sparsity. We consider a minimax-concave penalty-based formulation, which offers an unbiased estimate of the sparse signal. The resulting iterative firm-thresholding algorithm is restructured as a DNN architecture called FirmNet. The proposed network, FirmNet, has two interpretable shrinkage function parameters - one that controls the noise variance, and the other that allows for explicit sparsity control. We compare the network with a broader network architecture of Learned-ISTA (LISTA), and show that it outperforms in terms of the probability-of-error-in-support (PES) - a strong support recovery metric, by at least three-fold. We also observe an improvement of 2 to 4 dB in reconstruction SNR compared with LISTA.