We develop a lensless compressive imaging architecture, which consists of an aperture assembly and a single sensor, without using any lens. An anytime algorithm is proposed to reconstruct images from the compressive measurements; the algorithm produces a sequence of solutions that monotonically converge to the true signal (thus, anytime). The algorithm is developed based on the sparsity of local overlapping patches (in the transformation domain) and state-of-the-art results have been obtained. Experiments on real data demonstrate that encouraging results are obtained by measuring about 10% (of the image pixels) compressive measurements. The reconstruction results of the proposed algorithm are compared with the JPEG compression (based on file sizes) and the reconstructed image quality is close to the JPEG compression, in particular at a high compression rate.
We analyze the signal to noise ratio (SNR) in a recently proposed lensless compressive imaging architecture. The architecture consists of a sensor of a single detector element and an aperture assembly of an array of aperture elements, each of which has a programmable transmittance. This lensless compressive imaging architecture can be used in conjunction with compressive sensing to capture images in a compressed form of compressive measurements. In this paper, we perform noise analysis of this lensless compressive imaging architecture and compare it with pinhole aperture imaging and lens apert…
Lensless imaging is an important and challenging problem. One notable solution to lensless imaging is a single pixel camera which benefits from ideas central to compressive sampling. However, traditional single pixel cameras require many illumination patterns which result in a long acquisition process. Here we present a method for lensless imaging based on compressive ultrafast sensing. Each sensor acquisition is encoded with a different illumination pattern and produces a time series where time is a function of the photon's origin in the scene. Currently available hardware with picosecond tim…
We analyze the signal to noise ratio (SNR) in a lensless compressive imaging (LCI) architecture. The architecture consists of a sensor of a single detecting element and an aperture assembly of an array of programmable elements. LCI can be used in conjunction with compressive sensing to capture images in a compressed form of compressive measurements. In this paper, we perform SNR analysis of the LCI and compare it with imaging with a pinhole or a lens. We will show that the SNR in the LCI is independent of the image resolution, while the SNR in either pinhole aperture imaging or lens aperture i…
Multi-view images are acquired by a lensless compressive imaging architecture, which consists of an aperture assembly and multiple sensors. The aperture assembly consists of a two dimensional array of aperture elements whose transmittance can be individually controlled to implement a compressive sensing matrix. For each transmittance pattern of the aperture assembly, each of the sensors takes a measurement. The measurement vectors from the multiple sensors represent multi-view images of the same scene. We present theoretical framework for multi-view reconstruction and experimental results for …
The lensless endoscope is a promising device designed to image tissues in vivo at the cellular scale. The traditional acquisition setup consists in raster scanning during which the focused light beam from the optical fiber illuminates sequentially each pixel of the field of view (FOV). The calibration step to focus the beam and the sampling scheme both take time. In this preliminary work, we propose a scanning method based on compressive sampling theory. The method does not rely on a focused beam but rather on the random illumination patterns generated by the single-mode fibers. Experiments ar…
University of California, Berkeley（加州大学伯克利分校）；Orange Coast College（奥兰治海岸学院）
Compressive lensless imagers enable novel applications in an extremely compact device, requiring only a phase or amplitude mask placed close to the sensor. They have been demonstrated for 2D and 3D microscopy, single-shot video, and single-shot hyperspectral imaging; in each of these cases, a compressive-sensing-based inverse problem is solved in order to recover a 3D data-cube from a 2D measurement. Typically, this is accomplished using convex optimization and hand-picked priors. Alternatively, deep learning-based reconstruction methods offer the promise of better priors, but require many tho…
In this paper, we propose a lensless compressive imaging architecture. The architecture consists of two components, an aperture assembly and a sensor. No lens is used. The aperture assembly consists of a two dimensional array of aperture elements. The transmittance of each aperture element is independently controllable. The sensor is a single detection element. A compressive sensing matrix is implemented by adjusting the transmittance of the individual aperture elements according to the values of the sensing matrix. The proposed architecture is simple and reliable because no lens is used. The …
The existing lensless compressive camera ($\text{L}^2\text{C}^2$)~\cite{Huang13ICIP} suffers from low capture rates, resulting in low resolution images when acquired over a short time. In this work, we propose a new regime to mitigate these drawbacks. We replace the global-based compressive sensing used in the existing $\text{L}^2\text{C}^2$ by the local block (patch) based compressive sensing. We use a single sensor for each block, rather than for the entire image, thus forming a multiple but spatially parallel sensor $\text{L}^2\text{C}^2$. This new camera retains the advantages of existing …
UCLouvain（鲁汶大学）；Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel（艾克斯-马赛大学、法国国家科学研究中心、中央马赛学校、菲涅耳研究所）；Center of Molecular Imaging, Radiotherapy and Oncology (MIRO), IREC Institute, UCLouvain（分子影像、放疗与肿瘤学中心（MIRO），IREC研究所，鲁汶大学）；Lightcore Tehnologies（Lightcore Technologies公司）
The lensless endoscope (LE) is a promising device to acquire in vivo images at a cellular scale. The tiny size of the probe enables a deep exploration of the tissues. Lensless endoscopy with a multicore fiber (MCF) commonly uses a spatial light modulator (SLM) to coherently combine, at the output of the MCF, few hundreds of beamlets into a focus spot. This spot is subsequently scanned across the sample to generate a fluorescent image. We propose here a novel scanning scheme, partial speckle scanning (PSS), inspired by compressive sensing theory, that avoids the use of an SLM to perform fluores…
In this paper, we propose a lensless compressive sensing imaging architecture. The architecture consists of two components, an aperture assembly and a sensor. No lens is used. The aperture assembly consists of a two dimensional array of aperture elements. The transmittance of each aperture element is independently controllable. The sensor is a single detection element, such as a single photo-conductive cell. Each aperture element together with the sensor defines a cone of a bundle of rays, and the cones of the aperture assembly define the pixels of an image. Each pixel value of an image is the…
Lensless imaging seeks to replace/remove the lens in a conventional imaging system. The earliest cameras were in fact lensless, relying on long exposure times to form images on the other end of a small aperture in a darkened room/container (camera obscura). The introduction of a lens allowed for more light throughput and therefore shorter exposure times, while retaining sharp focus. The incorporation of digital sensors readily enabled the use of computational imaging techniques to post-process and enhance raw images (e.g. via deblurring, inpainting, denoising, sharpening). Recently, imaging sc…
Lensless imaging protects visual privacy by capturing heavily blurred images that are imperceptible for humans to recognize the subject but contain enough information for machines to infer information. Unfortunately, protecting visual privacy comes with a reduction in recognition accuracy and vice versa. We propose a learnable lensless imaging framework that protects visual privacy while maintaining recognition accuracy. To make captured images imperceptible to humans, we designed several loss functions based on total variation, invertibility, and the restricted isometry property. We studied t…
Lensless cameras are characterized by several advantages (e.g., miniaturization, ease of manufacture, and low cost) as compared with conventional cameras. However, they have not been extensively employed due to their poor image clarity and low image resolution, especially for tasks that have high requirements on image quality and details such as text detection and text recognition. To address the problem, a framework of deep-learning-based pipeline structure was built to recognize text with three steps from raw data captured by employing lensless cameras. This pipeline structure consisted of t…
Mask-based lensless cameras can be flat, thin, and light-weight, which makes them suitable for novel designs of computational imaging systems with large surface areas and arbitrary shapes. Despite recent progress in lensless cameras, the quality of images recovered from the lensless cameras is often poor due to the ill-conditioning of the underlying measurement system. In this paper, we propose to use coded illumination to improve the quality of images reconstructed with lensless cameras. In our imaging model, the scene/object is illuminated by multiple coded illumination patterns as the lensl…
University of California Riverside（加州大学河滨分校）；Carnegie Mellon University（卡内基梅隆大学）
Lensless cameras provide a framework to build thin imaging systems by replacing the lens in a conventional camera with an amplitude or phase mask near the sensor. Existing methods for lensless imaging can recover the depth and intensity of the scene, but they require solving computationally-expensive inverse problems. Furthermore, existing methods struggle to recover dense scenes with large depth variations. In this paper, we propose a lensless imaging system that captures a small number of measurements using different patterns on a programmable mask. In this context, we make three contributio…
Massachusetts Institute of Technology（麻省理工学院）；Singapore-MIT Alliance for Research and Technology (SMART) Centre（新加坡-麻省理工学院科研与技术联盟（SMART）中心）
Deep learning has been proven to yield reliably generalizable answers to numerous classification and decision tasks. Here, we demonstrate for the first time, to our knowledge, that deep neural networks (DNNs) can be trained to solve inverse problems in computational imaging. We experimentally demonstrate a lens-less imaging system where a DNN was trained to recover a phase object given a raw intensity image recorded some distance away.
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Lensless cameras are a class of imaging devices that shrink the physical dimensions to the very close vicinity of the image sensor by replacing conventional compound lenses with integrated flat optics and computational algorithms. Here we report a diffractive lensless camera with spatially-coded Voronoi-Fresnel phase to achieve superior image quality. We propose a design principle of maximizing the acquired information in optics to facilitate the computational reconstruction. By introducing an easy-to-optimize Fourier domain metric, Modulation Transfer Function volume (MTFv), which is related …
We demonstrate a compact and easy-to-build computational camera for single-shot 3D imaging. Our lensless system consists solely of a diffuser placed in front of a standard image sensor. Every point within the volumetric field-of-view projects a unique pseudorandom pattern of caustics on the sensor. By using a physical approximation and simple calibration scheme, we solve the large-scale inverse problem in a computationally efficient way. The caustic patterns enable compressed sensing, which exploits sparsity in the sample to solve for more 3D voxels than pixels on the 2D sensor. Our 3D voxel g…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
By replacing the lens with a thin optical element, lensless imaging enables new applications and solutions beyond those supported by traditional camera design and post-processing, e.g. compact and lightweight form factors and visual privacy. The latter arises from the highly multiplexed measurements of lensless cameras, which require knowledge of the imaging system to recover a recognizable image. In this work, we exploit this unique multiplexing property: casting the optics as an encoder that produces learned embeddings directly at the camera sensor. We do so in the context of image classific…
Null-Space Diffusion Distillation Unlocks Speed, Fidelity and Realism in Lensless Imaging
D3 Center, The University of Osaka（大阪大学D3中心）；The University of Osaka（大阪大学）；SANKEN, The University of Osaka（SANKEN与大阪大学）；Grad. Sch. of Eng. Sci., The University of Osaka（大阪大学工科科学院）
University of California, Berkeley（加州大学伯克利分校）；University of California, San Francisco（加州大学旧金山分校）
Mask-based lensless imagers are smaller and lighter than traditional lensed cameras. In these imagers, the sensor does not directly record an image of the scene; rather, a computational algorithm reconstructs it. Typically, mask-based lensless imagers use a model-based reconstruction approach that suffers from long compute times and a heavy reliance on both system calibration and heuristically chosen denoisers. In this work, we address these limitations using a bounded-compute, trainable neural network to reconstruct the image. We leverage our knowledge of the physical system by unrolling a tr…
Because image sensor chips have a finite bandwidth with which to read out pixels, recording video typically requires a trade-off between frame rate and pixel count. Compressed sensing techniques can circumvent this trade-off by assuming that the image is compressible. Here, we propose using multiplexing optics to spatially compress the scene, enabling information about the whole scene to be sampled from a row of sensor pixels, which can be read off quickly via a rolling shutter CMOS sensor. Conveniently, such multiplexing can be achieved with a simple lensless, diffuser-based imaging system. U…
Diffusion-driven lensless fiber endomicroscopic quantitative phase imaging towards digital pathology
Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University（同济大学上海智能自主系统研究院）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences（中国科学院苏州生物医学工程技术研究所）；School of Artificial Intelligence, OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University（西北工业大学人工智能与光电子学院）；Institute of Artificial Intelligence (TeleAI), China Telecom Corp Ltd（中国电信股份有限公司人工智能研究院）；Competence Center for Biomedical Computational Laser Systems (BIOLAS), TU Dresden（德累斯顿工业大学生物医学计算激光系统能力中心）；Laboratory of Measurement and Sensor System Technique (MST), TU Dresden（德累斯顿工业大学测量与传感器系统技术实验室）
University of California, Berkeley（加利福尼亚大学伯克利分校）；UCB/UCSF Joint Graduate Program in Bioengineering（加州大学伯克利分校/加州大学旧金山分校联合生物工程研究生项目）
Hyperspectral imaging is useful for applications ranging from medical diagnostics to agricultural crop monitoring; however, traditional scanning hyperspectral imagers are prohibitively slow and expensive for widespread adoption. Snapshot techniques exist but are often confined to bulky benchtop setups or have low spatio-spectral resolution. In this paper, we propose a novel, compact, and inexpensive computational camera for snapshot hyperspectral imaging. Our system consists of a tiled spectral filter array placed directly on the image sensor and a diffuser placed close to the sensor. Each poi…
LensNet: An End-to-End Learning Framework for Empirical Point Spread Function Modeling and Lensless Imaging Reconstruction
Faculty of Science and Technology, University of Macau（澳门大学科技学院）；Shanghai University（上海大学）；School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University（上海交通大学电子信息与电气工程学院）；School of Computer Science and Engineering, Huizhou University（惠州大学计算机科学与工程学院）
Recently, coded masks have been used to demonstrate a thin form-factor lensless camera, FlatCam, in which a mask is placed immediately on top of a bare image sensor. In this paper, we present an imaging model and algorithm to jointly estimate depth and intensity information in the scene from a single or multiple FlatCams. We use a light field representation to model the mapping of 3D scene onto the sensor in which light rays from different depths yield different modulation patterns. We present a greedy depth pursuit algorithm to search the 3D volume and estimate the depth and intensity of each…
Photography usually requires optics in conjunction with a recording device (an image sensor). Eliminating the optics could lead to new form factors for cameras. Here, we report a simple demonstration of imaging using a bare CMOS sensor that utilizes computation. The technique relies on the space variant point-spread functions resulting from the interaction of a point source in the field of view with the image sensor. These space-variant point-spread functions are combined with a reconstruction algorithm in order to image simple objects displayed on a discrete LED array as well as on an LCD scr…
Computational compressive imaging reconstruction with a simulated-annealing-based Ising solver
Institute for Quantum Sensing and Information Processing, State Key Laboratory of Photonics and Communications, Shanghai Jiao Tong University（上海交通大学生物医学工程学院）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究与探索中心）
Lensless imaging has emerged as a potential solution towards realizing ultra-miniature cameras by eschewing the bulky lens in a traditional camera. Without a focusing lens, the lensless cameras rely on computational algorithms to recover the scenes from multiplexed measurements. However, the current iterative-optimization-based reconstruction algorithms produce noisier and perceptually poorer images. In this work, we propose a non-iterative deep learning based reconstruction approach that results in orders of magnitude improvement in image quality for lensless reconstructions. Our approach, ca…
Arizona State University（亚利桑那州立大学）；SenseBrain Technology（商汤科技（SenseBrain Technology））
The lensless pinhole camera is perhaps the earliest and simplest form of an imaging system using only a pinhole-sized aperture in place of a lens. They can capture an infinite depth-of-field and offer greater freedom from optical distortion over their lens-based counterparts. However, the inherent limitations of a pinhole system result in lower sharpness from blur caused by optical diffraction and higher noise levels due to low light throughput of the small aperture, requiring very long exposure times to capture well-exposed images. In this paper, we explore an image restoration pipeline using…
Integrated Forward-Inverse Network for Lensless Image Reconstruction
Department of Mechanical Engineering, Seoul National University（韩国首尔国立大学机械工程系）；School of Mechanical and Aerospace Engineering/SNU-IAMD, Seoul National University（韩国首尔国立大学机械与航空航天工程学院/SNU-IAMD）；Department of Electrical and Electronic Engineering, Yonsei University（韩国延世大学电气与电子工程系）；Department of Biomedical Engineering, University of Michigan（美国密歇根大学安娜堡分校生物医学工程系）
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Lensless imaging can provide visual privacy due to the highly multiplexed characteristic of its measurements. However, this alone is a weak form of security, as various adversarial attacks can be designed to invert the one-to-many scene mapping of such cameras. In this work, we enhance the privacy provided by lensless imaging by (1) downsampling at the sensor and (2) using a programmable mask with variable patterns as our optical encoder. We build a prototype from a low-cost LCD and Raspberry Pi components, for a total cost of around 100 USD. This very low price point allows our system to be d…
The author intends to provide you with a beautiful, elegant, user-friendly cookbook for mathematics in Snapshot Compressive Imaging (SCI). Currently, the cookbook is composed of introduction, conventional optimization, and deep equilibrium models. The latest releases are strongly recommended! For any other questions, suggestions, or comments, feel free to email the author.
Compressive sensing is a new technology for modern computational imaging systems. In comparison to widespread conventional image sensing, the compressive imaging paradigm requires specific forensic analysis techniques and tools. In this regards, one of basic scenarios in image forensics is to distinguish traditionally sensed images from sophisticated compressively sensed ones. To do this, we first mathematically and systematically model the imaging system based on compressive sensing technology. Afterwards, a simplified version of the whole model is presented, which is appropriate for forensic…
Tsinghua University（清华大学）；Nokia Bell Labs（诺基亚贝尔实验室）；Duke University（杜克大学）
Snapshot compressive imaging (SCI) refers to compressive imaging systems where multiple frames are mapped into a single measurement, with video compressive imaging and hyperspectral compressive imaging as two representative applications. Though exciting results of high-speed videos and hyperspectral images have been demonstrated, the poor reconstruction quality precludes SCI from wide applications.This paper aims to boost the reconstruction quality of SCI via exploiting the high-dimensional structure in the desired signal. We build a joint model to integrate the nonlocal self-similarity of vid…
UCLouvain（天主教鲁汶大学）；Instituto de Telecomunicações（葡萄牙电信研究所）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等理工学院）
Single Pixel (SP) imaging is now a reality in many applications, e.g., biomedical ultrathin endoscope and fluorescent spectroscopy. In this context, many schemes exist to improve the light throughput of these device, e.g., using structured illumination driven by compressive sensing theory. In this work, we consider the combination of SP imaging with Fourier Transform Interferometry (SP-FTI) to reach high-resolution HyperSpectral (HS) imaging, as desirable, e.g., in fluorescent spectroscopy. While this association is not new, we here focus on optimizing the spatial illumination, structured as H…
Georgia Institute of Technology（佐治亚理工学院）；The Ohio State University（俄亥俄州立大学）
We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a hidden Markov tree (HMT) but, unlike other works, ours is based on loopy belief propagation (LBP). For LBP, we adopt a recently proposed "turbo" message passing schedule that alternates between exploitation of HMT structure and exploitation of compressive-measurement structure. For the latter, we leverage Donoho, Maleki, and Montanari's recently proposed ap…
Universidad Industrial de Santander（桑坦德工业大学）；Stanford University（斯坦福大学）
Compressive imaging using coded apertures (CA) is a powerful technique that can be used to recover depth, light fields, hyperspectral images and other quantities from a single snapshot. The performance of compressive imaging systems based on CAs mostly depends on two factors: the properties of the mask's attenuation pattern, that we refer to as "codification" and the computational techniques used to recover the quantity of interest from the coded snapshot. In this work, we introduce the idea of using time-varying CAs synchronized with spatially varying pixel shutters. We divide the exposure of…
Compressive sensing is considered a huge breakthrough in signal acquisition. It allows recording an image consisting of $N^2$ pixels using much fewer than $N^2$ measurements if it can be transformed to a basis where most pixels take on negligibly small values. Standard compressive sensing techniques suffer from the computational overhead needed to reconstruct an image with typical computation times between hours and days and are thus not optimal for applications in physics and spectroscopy. We demonstrate an adaptive compressive sampling technique that performs measurements directly in a spars…
Duke University（杜克大学）；Fitzpatrick Institute for Photonics（菲茨帕特里克光子学研究所）
We use mechanical translation of a coded aperture for code division multiple access compression of video. We present experimental results for reconstruction at 148 frames per coded snapshot.
Recently, deep learning-based compressive imaging (DCI) has surpassed the conventional compressive imaging in reconstruction quality and faster running time. While multi-scale has shown superior performance over single-scale, research in DCI has been limited to single-scale sampling. Despite training with single-scale images, DCI tends to favor low-frequency components similar to the conventional multi-scale sampling, especially at low subrate. From this perspective, it would be easier for the network to learn multi-scale features with a multi-scale sampling architecture. In this work, we prop…
Case Western Reserve University（凯斯西储大学）；Commonwealth Scientific and Industrial Research Organisation (CSIRO)（联邦科学与工业研究组织（CSIRO））；University of Queensland（昆士兰大学）；University of New South Wales（新南威尔士大学）
In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using dictionary learning. We then perform an SVD on the dictionary and use the first few left singular vectors as the rows of the measurement matrix to obtain the compressive measurements for reconstruction. The proposed method provides significant improvement over the conventional compressive sensing approaches. The reconstruction performance is further improve…
A limitation of many compressive imaging architectures lies in the sequential nature of the sensing process, which leads to long sensing times. In this paper we present a novel architecture that uses fewer detectors than the number of reconstructed pixels and is able to acquire the image in a single acquisition. This paves the way for the development of video architectures that acquire several frames per second. We specifically address the diffraction problem, showing that deconvolution normally used to recover diffraction blur can be replaced by convolution of the sensing matrix, and how meas…
IRIT UMR CNRS 5505（法国国家科学研究中心IRIT联合研究单元（UMR 5505））；University of Toulouse（图卢兹大学）
The interest of compressive sampling in ultrasound imaging has been recently extensively evaluated by several research teams. Following the different application setups, it has been shown that the RF data may be reconstructed from a small number of measurements and/or using a reduced number of ultrasound pulse emissions. Nevertheless, RF image spatial resolution, contrast and signal to noise ratio are affected by the limited bandwidth of the imaging transducer and the physical phenomenon related to US wave propagation. To overcome these limitations, several deconvolution-based image processing…
Compressive imaging aims to recover a latent image from under-sampled measurements, suffering from a serious ill-posed inverse problem. Recently, deep neural networks have been applied to this problem with superior results, owing to the learned advanced image priors. These approaches, however, require training separate models for different imaging modalities and sampling ratios, leading to overfitting to specific settings. In this paper, a dynamic proximal unrolling network (dubbed DPUNet) was proposed, which can handle a variety of measurement matrices via one single model without retraining.…
University of California, Berkeley（加州大学伯克利分校）；Mitsubishi Electric Research Laboratories (MERL)（三菱电机研究实验室）
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon, which makes the method preferable in applications where linear measurement models are inaccurate. We construct the measurement model by expanding the scattered wave-field with an accelerated-gradient method, which is guaranteed to converge and is suitable for large-scale problems. We provide explicit formulas for computing the gradient of our measurement mo…
Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学学院）；School of Mathematical Science, University of Electronic Science and Technology of China（电子科技大学数学科学学院）
Transform image processing methods are methods that work in domains of image transforms, such as Discrete Fourier, Discrete Cosine, Wavelet and alike. They are the basic tool in image compression, in image restoration, in image re-sampling and geometrical transformations and can be traced back to early 1970-ths. The paper presents a review of these methods with emphasis on their comparison and relationships, from the very first steps of transform image compression methods to adaptive and local adaptive transform domain filters for image restoration, to methods of precise image re-sampling and …
