arXiv subjects

Shirin Jalali

Publications and source records attributed to Shirin Jalali.

At least 19 recordsLinked to original sources

arXiv2026

Maximum Likelihood Reconstruction for Multi-Look Digital Holography with Markov-Modeled Speckle Correlation

Multi-look acquisition is a widely used strategy for reducing speckle noise in coherent imaging systems such as digital holography. By acquiring multiple measurements, speckle can be suppressed through averaging or joint reconstruction, typically under the assumption that speckle realizations across looks are statistically independent. In practice, however, hardware constraints limit measurement diversity, leading to inter-look correlation that degrades the performance of conventional methods. In this work, we study the reconstruction of speckle-free reflectivity from complex-valued multi-look measurements in the presence of correlated speckle. We model the inter-look dependence using a first-order Markov process and derive the corresponding likelihood under a first-order Markov approximation, resulting in a constrained maximum likelihood estimation problem. To solve this problem, we develop an efficient projected gradient descent framework that combines gradient-based updates with implicit regularization via deep image priors, and leverages Monte Carlo approximation and matrix-free operators for scalable computation. Simulation results demonstrate that the proposed approach remains robust under strong inter-look correlation, achieving performance close to the ideal independent-look scenario and consistently outperforming methods that ignore such dependencies. These results highlight the importance of explicitly modeling inter-look correlation and provide a practical framework for multi-look holographic reconstruction under realistic acquisition conditions. Our code is available at: https://github.com/Computational-Imaging-RU/MLE-Holography-Markov.

eess.IV↗

arXiv2026

Deep Learning-Based Snow Depth Retrieval Using Sentinel-1 Repeat-Pass InSAR

Snow depth plays a central role in seasonal snowpack characterization and the terrestrial water cycle, yet remains challenging to estimate at high spatial resolution. Recent studies have shown that repeat-pass interferometric synthetic aperture radar (InSAR) measurements combined with physics-based models can enable effective snow water equivalent (SWE) retrieval. However, the performance of these methods depends strongly on measurement accuracy and modeling assumptions. Building on the success of InSAR-based approaches, we develop a robust learning-based model that directly learns the relationship between measured InSAR observables and snow depth. The model is trained on a single SnowEx Idaho site and evaluated across independent years and geographically distinct regions. Results demonstrate strong temporal and spatial transferability. In temporal transfer experiments, the proposed approach achieves a Pearson correlation of 0.81 with lidar snow depth, compared to a correlation of approximately 0.47 reported for physics-based Sentinel-1 SWE retrievals over the same site.

cs.CE↗

arXiv2026

Shot-Aware Frame Sampling for Video Understanding

Video frame sampling is essential for efficient long-video understanding with Vision-Language Models (VLMs), since dense inputs are costly and often exceed context limits. Yet when only a small number of frames can be retained, existing samplers often fail to balance broad video coverage with brief but critical events, which can lead to unreliable downstream predictions. To address this issue, we present InfoShot, a task-agnostic, shot-aware frame sampler for long-video understanding. InfoShot first partitions a video into semantically consistent shots, and then selects two complementary keyframes from each shot: one to represent the main content and one to capture unusual within-shot changes. This design is guided by an information-theoretic objective that encourages the sampled set to retain high information about both shot structure and sparse within-shot deviations. In this way, it improves the chance of preserving both overall video context and short decision-critical moments without requiring any retraining. To better evaluate such short-lived events, we further introduce SynFlash, a synthetic benchmark with controllable sub-second anomaly patterns and frame-level ground truth, and we also evaluate InfoShot on existing anomaly datasets and general video understanding tasks. Experiments show that InfoShot improves anomaly hit rate and downstream Video-QA accuracy under frame number constraints, while matching or outperforming strong baselines on standard video understanding benchmarks.

cs.CV↗

arXiv2026

Monte Carlo Maximum Likelihood Reconstruction for Digital Holography with Speckle

In coherent imaging, speckle is statistically modeled as multiplicative noise, posing a fundamental challenge for image reconstruction. While maximum likelihood estimation (MLE) provides a principled framework for speckle mitigation, its application to coherent imaging system such as digital holography with finite apertures is hindered by the prohibitive cost of high-dimensional matrix inversion, especially at high resolutions. This computational burden has prevented the use of MLE-based reconstruction with physically accurate aperture modeling. In this work, we propose a randomized linear algebra approach that enables scalable MLE optimization without explicit matrix inversions in gradient computation. By exploiting the structural properties of sensing matrix and using conjugate gradient for likelihood gradient evaluation, the proposed algorithm supports accurate aperture modeling without the simplifying assumptions commonly imposed for tractability. We term the resulting method projected gradient descent with Monte Carlo estimation (PGD-MC). The proposed PGD-MC framework (i) demonstrates robustness to diverse and physically accurate aperture models, (ii) achieves substantial improvements in reconstruction quality and computational efficiency, and (iii) scales effectively to high-resolution digital holography. Extensive experiments incorporating three representative denoisers as regularization show that PGD-MC provides a flexible and effective MLE-based reconstruction framework for digital holography with finite apertures, consistently outperforming prior Plug-and-Play model-based iterative reconstruction methods in both accuracy and speed. Our code is available at: https://github.com/Computational-Imaging-RU/MC_Maximum_Likelihood_Digital_Holography_Speckle.

cs.CV↗

arXiv2025

Zero-shot Denoising via Neural Compression: Theoretical and algorithmic framework

Zero-shot denoising aims to denoise observations without access to training samples or clean reference images. This setting is particularly relevant in practical imaging scenarios involving specialized domains such as medical imaging or biology. In this work, we propose the Zero-Shot Neural Compression Denoiser (ZS-NCD), a novel denoising framework based on neural compression. ZS-NCD treats a neural compression network as an untrained model, optimized directly on patches extracted from a single noisy image. The final reconstruction is then obtained by aggregating the outputs of the trained model over overlapping patches. Thanks to the built-in entropy constraints of compression architectures, our method naturally avoids overfitting and does not require manual regularization or early stopping. Through extensive experiments, we show that ZS-NCD achieves state-of-the-art performance among zero-shot denoisers for both Gaussian and Poisson noise, and generalizes well to both natural and non-natural images. Additionally, we provide new finite-sample theoretical results that characterize upper bounds on the achievable reconstruction error of general maximum-likelihood compression-based denoisers. These results further establish the theoretical foundations of compression-based denoising. Our code is available at: https://github.com/Computational-Imaging-RU/ZS-NCDenoiser.

eess.IV↗

arXiv2025

Multilook Coherent Imaging: Theoretical Guarantees and Algorithms

Multilook coherent imaging is a widely used technique in applications such as digital holography, ultrasound imaging, and synthetic aperture radar. A central challenge in these systems is the presence of multiplicative noise, commonly known as speckle, which degrades image quality. Despite the widespread use of coherent imaging systems, their theoretical foundations remain relatively underexplored. In this paper, we study both the theoretical and algorithmic aspects of likelihood-based approaches for multilook coherent imaging, providing a rigorous framework for analysis and method development. Our theoretical contributions include establishing the first theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our results capture the dependence of MSE on the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we employ projected gradient descent (PGD) as an efficient method for computing the maximum likelihood solution. Furthermore, we introduce two key ideas to enhance the practical performance of PGD. First, we incorporate the Newton-Schulz algorithm to compute matrix inverses within the PGD iterations, significantly reducing computational complexity. Second, we develop a bagging strategy to mitigate projection errors introduced during PGD updates. We demonstrate that combining these techniques with PGD yields state-of-the-art performance. Our code is available at https://github.com/Computational-Imaging-RU/Bagged-DIP-Speckle.

stat.ML↗

arXiv2025

DeCompress: Denoising via Neural Compression

Learning-based denoising algorithms achieve state-of-the-art performance across various denoising tasks. However, training such models relies on access to large training datasets consisting of clean and noisy image pairs. On the other hand, in many imaging applications, such as microscopy, collecting ground truth images is often infeasible. To address this challenge, researchers have recently developed algorithms that can be trained without requiring access to ground truth data. However, training such models remains computationally challenging and still requires access to large noisy training samples. In this work, inspired by compression-based denoising and recent advances in neural compression, we propose a new compression-based denoising algorithm, which we name DeCompress, that i) does not require access to ground truth images, ii) does not require access to large training dataset - only a single noisy image is sufficient, iii) is robust to overfitting, and iv) achieves superior performance compared with zero-shot or unsupervised learning-based denoisers.

eess.IV↗

arXiv2025

Bayesian Despeckling of Structured Sources

Speckle noise is a fundamental challenge in coherent imaging systems, significantly degrading image quality. Over the past decades, numerous despeckling algorithms have been developed for applications such as Synthetic Aperture Radar (SAR) and digital holography. In this paper, we aim to establish a theoretically grounded approach to despeckling. We propose a method applicable to general structured stationary stochastic sources. We demonstrate the effectiveness of the proposed method on piecewise constant sources. Additionally, we theoretically derive a lower bound on the despeckling performance for such sources. The proposed depseckler applied to the 1-Markov structured sources achieves better reconstruction performance with no strong simplification of the ground truth signal model or speckle noise.

cs.IT↗

arXiv2025

Snapshot Compressive Imaging under Saturation: Theory, Mask Design, and Reconstruction

Snapshot compressive imaging (SCI) acquires high-dimensional data cubes, such as videos and hyperspectral images, by optically multiplexing multiple coded frames into a single two-dimensional measurement. While this multiplexing enables high acquisition efficiency, it also increases the risk of sensor saturation: the accumulated intensity may exceed the detector dynamic range, causing clipped measurements that violate the standard linear SCI model. This paper studies SCI reconstruction under such saturated measurements from both theoretical and algorithmic perspectives. We model saturation as an element-wise clipping nonlinearity and derive a finite-sample recovery bound for compression-based SCI. The bound explicitly relates the reconstruction error to the Bernoulli mask density, the compression rate of the signal class, measurement noise, and the expected fraction of saturated measurements. The analysis reveals a principled mask-design rule: under saturation, the optimal Bernoulli mask density remains below one-half and decreases as saturation becomes stronger. Motivated by this result, we optimize mask patterns for saturated acquisition and introduce a saturation-aware plug-and-play reconstruction framework, termed \emph{Saturation-Aware PnP Net} (SAPnet), which enforces consistency with both unsaturated and clipped measurements. Experiments on standard video SCI benchmarks validate the theoretical predictions and show that SAPnet substantially improves reconstruction quality over conventional PnP-based methods, especially in strongly saturated regimes.

eess.IV↗

arXiv2025

Theoretical Characterization of Effect of Masks in Snapshot Compressive Imaging

Snapshot compressive imaging (SCI) refers to the recovery of three-dimensional data cubes-such as videos or hyperspectral images-from their two-dimensional projections, which are generated by a special encoding of the data with a mask. SCI systems commonly use binary-valued masks that follow certain physical constraints. Optimizing these masks subject to these constraints is expected to improve system performance. However, prior theoretical work on SCI systems focuses solely on independently and identically distributed (i.i.d.) Gaussian masks, which do not permit such optimization. On the other hand, existing practical mask optimizations rely on computationally intensive joint optimizations that provide limited insight into the role of masks and are expected to be sub-optimal due to the non-convexity and complexity of the optimization. In this paper, we analytically characterize the performance of SCI systems employing binary masks and leverage our analysis to optimize hardware parameters. Our findings provide a comprehensive and fundamental understanding of the role of binary masks - with both independent and dependent elements - and their optimization. We also present simulation results that confirm our theoretical findings and further illuminate different aspects of mask design.

cs.IT↗

arXiv2025

Comprehensive Examination of Unrolled Networks for Solving Linear Inverse Problems

Unrolled networks have become prevalent in various computer vision and imaging tasks. Although they have demonstrated remarkable efficacy in solving specific computer vision and computational imaging tasks, their adaptation to other applications presents considerable challenges. This is primarily due to the multitude of design decisions that practitioners working on new applications must navigate, each potentially affecting the network's overall performance. These decisions include selecting the optimization algorithm, defining the loss function, and determining the number of convolutional layers, among others. Compounding the issue, evaluating each design choice requires time-consuming simulations to train, fine-tune the neural network, and optimize for its performance. As a result, the process of exploring multiple options and identifying the optimal configuration becomes time-consuming and computationally demanding. The main objectives of this paper are (1) to unify some ideas and methodologies used in unrolled networks to reduce the number of design choices a user has to make, and (2) to report a comprehensive ablation study to discuss the impact of each of the choices involved in designing unrolled networks and present practical recommendations based on our findings. We anticipate that this study will help scientists and engineers design unrolled networks for their applications and diagnose problems within their networks efficiently.

eess.IV↗

arXiv2024

Untrained Neural Nets for Snapshot Compressive Imaging: Theory and Algorithms

Snapshot compressive imaging (SCI) recovers high-dimensional (3D) data cubes from a single 2D measurement, enabling diverse applications like video and hyperspectral imaging to go beyond standard techniques in terms of acquisition speed and efficiency. In this paper, we focus on SCI recovery algorithms that employ untrained neural networks (UNNs), such as deep image prior (DIP), to model source structure. Such UNN-based methods are appealing as they have the potential of avoiding the computationally intensive retraining required for different source models and different measurement scenarios. We first develop a theoretical framework for characterizing the performance of such UNN-based methods. The theoretical framework, on the one hand, enables us to optimize the parameters of data-modulating masks, and on the other hand, provides a fundamental connection between the number of data frames that can be recovered from a single measurement to the parameters of the untrained NN. We also employ the recently proposed bagged-deep-image-prior (bagged-DIP) idea to develop SCI Bagged Deep Video Prior (SCI-BDVP) algorithms that address the common challenges faced by standard UNN solutions. Our experimental results show that in video SCI our proposed solution achieves state-of-the-art among UNN methods, and in the case of noisy measurements, it even outperforms supervised solutions.

cs.CV↗

arXiv2024

Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise

We investigate both the theoretical and algorithmic aspects of likelihood-based methods for recovering a complex-valued signal from multiple sets of measurements, referred to as looks, affected by speckle (multiplicative) noise. Our theoretical contributions include establishing the first existing theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our theoretical results capture the dependence of MSE upon the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we introduce the concept of bagged Deep Image Priors (Bagged-DIP) and integrate them with projected gradient descent. Furthermore, we show how employing Newton-Schulz algorithm for calculating matrix inverses within the iterations of PGD reduces the computational complexity of the algorithm. We will show that this method achieves the state-of-the-art performance.

cs.IT↗

arXiv2023

On convergence and optimality of maximum-likelihood APA

Affine projection algorithm (APA) is a well-known algorithm in adaptive filtering applications such as audio echo cancellation. APA relies on three parameters: $P$ (projection order), $μ$ (step size) and $δ$ (regularization parameter). It is known that running APA for a fixed set of parameters leads to a tradeoff between convergence speed and accuracy. Therefore, various methods for adaptively setting the parameters have been proposed in the literature. Inspired by maximum likelihood (ML) estimation, we derive a new ML-based approach for adaptively setting the parameters of APA, which we refer to as ML-APA. For memoryless Gaussian inputs, we fully characterize the expected misalignment error of ML-APA as a function of iteration number and show that it converges to zero as $O({1\over t})$. We further prove that the achieved error is asymptotically optimal. ML-APA updates its estimate once every $P$ samples. We also propose incremental ML-APA (IML-APA), which updates the coefficients at every time step and outperforms ML-APA in our simulations results. Our simulation results verify the analytical conclusions for memoryless inputs and show that the new algorithms also perform well for strongly correlated input signals.

cs.IT↗

arXiv2023

Theoretical Analysis of Binary Masks in Snapshot Compressive Imaging Systems

Snapshot compressive imaging (SCI) systems have gained significant attention in recent years. While previous theoretical studies have primarily focused on the performance analysis of Gaussian masks, practical SCI systems often employ binary-valued masks. Furthermore, recent research has demonstrated that optimized binary masks can significantly enhance system performance. In this paper, we present a comprehensive theoretical characterization of binary masks and their impact on SCI system performance. Initially, we investigate the scenario where the masks are binary and independently identically distributed (iid), revealing a noteworthy finding that aligns with prior numerical results. Specifically, we show that the optimal probability of non-zero elements in the masks is smaller than 0.5. This result provides valuable insights into the design and optimization of binary masks for SCI systems, facilitating further advancements in the field. Additionally, we extend our analysis to characterize the performance of SCI systems where the mask entries are not independent but are generated based on a stationary first-order Markov process. Overall, our theoretical framework offers a comprehensive understanding of the performance implications associated with binary masks in SCI systems.

cs.IT↗

arXiv2021

Compressed sensing in the presence of speckle noise

The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The current acquisition technology oversamples signals and converts the problem into a denoising problem with multiplicative noise. However, this paper explores the possibility of reducing the number of measurements below the ambient dimension of the signal. The sophistications that appear in the study of multiplicative noises have so far impeded theoretical analysis of such problems. This paper aims to present the first theoretical result regarding the recovery of signals from their undersampled measurements under the speckle noise. It is shown that if the signal class is structured, in the sense that the signals can be compressed efficiently, then one can obtain accurate estimates of the signal from fewer measurements than the ambient dimension. We demonstrate the effectiveness of the methods we propose through simulation results.

cs.IT↗

arXiv2020

GAP-net for Snapshot Compressive Imaging

Snapshot compressive imaging (SCI) systems aim to capture high-dimensional ($\ge3$D) images in a single shot using 2D detectors. SCI devices include two main parts: a hardware encoder and a software decoder. The hardware encoder typically consists of an (optical) imaging system designed to capture {compressed measurements}. The software decoder on the other hand refers to a reconstruction algorithm that retrieves the desired high-dimensional signal from those measurements. In this paper, using deep unfolding ideas, we propose an SCI recovery algorithm, namely GAP-net, which unfolds the generalized alternating projection (GAP) algorithm. At each stage, GAP-net passes its current estimate of the desired signal through a trained convolutional neural network (CNN). The CNN operates as a denoiser that projects the estimate back to the desired signal space. For the GAP-net that employs trained auto-encoder-based denoisers, we prove a probabilistic global convergence result. Finally, we investigate the performance of GAP-net in solving video SCI and spectral SCI problems. In both cases, GAP-net demonstrates competitive performance on both synthetic and real data. In addition to having high accuracy and high speed, we show that GAP-net is flexible with respect to signal modulation implying that a trained GAP-net decoder can be applied in different systems. Our code is at https://github.com/mengziyi64/ADMM-net.

eess.IV↗

arXiv2020

Using Black-box Compression Algorithms for Phase Retrieval

Compressive phase retrieval refers to the problem of recovering a structured $n$-dimensional complex-valued vector from its phase-less under-determined linear measurements. The non-linearity of measurements makes designing theoretically-analyzable efficient phase retrieval algorithms challenging. As a result, to a great extent, algorithms designed in this area are developed to take advantage of simple structures such as sparsity and its convex generalizations. The goal of this paper is to move beyond simple models through employing compression codes. Such codes are typically developed to take advantage of complex signal models to represent the signals as efficiently as possible. In this work, it is shown how an existing compression code can be treated as a black box and integrated into an efficient solution for phase retrieval. First, COmpressive PhasE Retrieval (COPER) optimization, a computationally-intensive compression-based phase retrieval method, is proposed. COPER provides a theoretical framework for studying compression-based phase retrieval. The number of measurements required by COPER is connected to $κ$, the $α$-dimension (closely related to the rate-distortion dimension) of the given family of compression codes. To finds the solution of COPER, an efficient iterative algorithm called gradient descent for COPER (GD-COPER) is proposed. It is proven that under some mild conditions on the initialization, if the number of measurements is larger than $ C κ^2 \log^2 n$, where $C$ is a constant, GD-COPER obtains an accurate estimate of the input vector in polynomial time. In the simulation results, JPEG2000 is integrated in GD-COPER to confirm the superb performance of the resulting algorithm on real-world images.

cs.IT↗