Alfred Bruckstein - Academia.edu (original) (raw)

Papers by Alfred Bruckstein

Research paper thumbnail of E. Rivlin Department of Computer Science Israel Institute of Technology Technion Haifa, Israel

In this paper we discuss a new approach to invariant signatures for recognizing curves under view... more In this paper we discuss a new approach to invariant signatures for recognizing curves under viewing distortions and partial occlusion. The approach is intended to overcome the ill-posed problem of nding derivatives, on which local invariants usually depend. The basic idea is to use invariant nite di erences, with a scale parameter that determines the size of the di erencing interval. The scale parameter is allowed to vary so that we obtain a\ scale space"-like invariant representation of the curve, with larger di erence ...

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Research paper thumbnail of Two-Image Perspective Photometric Stereo Using Shape-from-Shading

Lecture Notes in Computer Science, 2013

ABSTRACT Shape-from-Shading and photometric stereo are two fundamental problems in Computer Visio... more ABSTRACT Shape-from-Shading and photometric stereo are two fundamental problems in Computer Vision aimed at reconstructing surface depth given either a single image taken under a known light source or multiple images taken under different illuminations, respectively. Whereas the former utilizes partial differential equation (PDE) techniques to solve the image irradiance equation, the latter can be expressed as a linear system of equations in surface derivatives when 3 or more images are given. It therefore seems that current photometric stereo techniques do not extract all possible depth information from each image by itself. This paper utilizes PDE techniques for the solution of the combined Shape-from-Shading and photometric stereo problem when only 2 images are available. Extending our previous results on this problem, we consider the more realistic perspective projection of surfaces during the photographic process. Under these assumptions, there is a unique weak (Lipschitz continuous) solution to the problem at hand, solving the well known convex/concave ambiguity of the Shape-from-Shading problem. We propose two approximation schemes for the numerical solution of this problem, an up-wind finite difference scheme and a Semi-Lagrangian scheme, and analyze their properties. We show that both schemes converge linearly and accurately reconstruct the original surfaces. In comparison with a similar method for the orthographic 2-image photometric stereo, the proposed perspective one outperforms the orthographic one. We also demonstrate the method on real-life images. Our results thus show that using methodologies common in the field of Shape-from-Shading it is possible to recover more depth information for the photometric stereo problem under the more realistic perspective projection assumption.

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Research paper thumbnail of Holographic Sensing

Holographic representations of data encode information in packets of equal importance that enable... more Holographic representations of data encode information in packets of equal importance that enable progressive recovery. The quality of recovered data improves as more and more packets become available. This progressive recovery of the information is independent of the order in which packets become available. Such representations are ideally suited for distributed storage and for the transmission of data packets over networks with unpredictable delays and or erasures. Several methods for holographic representations of signals and images have been proposed over the years and multiple description information theory also deals with such representations. Surprisingly, however, these methods had not been considered in the classical framework of optimal least-squares estimation theory, until very recently. We develop a least-squares approach to the design of holographic representation for stochastic data vectors, relying on the framework widely used in modeling signals and images.

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Research paper thumbnail of Pincer-based vs. Same-direction Search Strategies After Smart Evaders by Swarms of Agents

Suppose in a given planar region, there are smart mobile evaders and we want to detect them using... more Suppose in a given planar region, there are smart mobile evaders and we want to detect them using sweeping agents. We assume that the agents have line sensors of equal length. We propose procedures for designing cooperative sweeping processes that ensure successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a known limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity the sweeping agent must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present a quantitative and qualitative comparison a...

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Research paper thumbnail of Holographic Image Sensing

Holographic representations of data enable distributed storage with progressive refinement when t... more Holographic representations of data enable distributed storage with progressive refinement when the stored packets of data are made available in any arbitrary order. In this paper, we propose and test patch-based transform coding holographic sensing of image data. Our proposal is optimized for progressive recovery under random order of retrieval of the stored data. The coding of the image patches relies on the design of distributed projections ensuring best image recovery, in terms of the ℓ_2 norm, at each retrieval stage. The performance depends only on the number of data packets that has been retrieved thus far. Several possible options to enhance the quality of the recovery while changing the size and number of data packets are discussed and tested. This leads us to examine several interesting bit-allocation and rate-distortion trade offs, highlighted for a set of natural images with ensemble estimated statistical properties.

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Research paper thumbnail of Search for smart evaders with sweeping agents

Robotica, 2021

Suppose in a given planar circular region, there are smart mobile evaders and we want to find the... more Suppose in a given planar circular region, there are smart mobile evaders and we want to find them using sweeping agents. We assume the sweeping agents are in a line formation whose total length is predetermined. We propose procedures for designing a sweeping process that ensures the successful completion of the task, thereby deriving conditions on the sweeping velocity of the linear formation and its path. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. We present results on the search time given the initial conditions.

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Research paper thumbnail of Direct Shape Recovery from Photometric Stereo with Shadows

2013 International Conference on 3D Vision, 2013

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Research paper thumbnail of From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images

SIAM Review, 2009

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Research paper thumbnail of Optimized Overlay Metrology Marks: Theory and Experiment

IEEE Transactions on Semiconductor Manufacturing, 2004

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Research paper thumbnail of Design of shapes for precise image registration

IEEE Transactions on Information Theory, 1998

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Research paper thumbnail of Artificial intelligence and computer vision: proceedings of the seventh Israeli conference, 26-27 December, 1990, Ramat Gan, Israel

Structuring Events for their Pronominal Reference. Monitoring the Execution of Contextualised Exp... more Structuring Events for their Pronominal Reference. Monitoring the Execution of Contextualised Expianations. Exact Point Matching. Similarity-Invariant Recognition of Partially Occluded Planar Curves and Shapes. Robust Estimators in Computer Vision: An Introduction to Least Median of Squares Regression. On Optimal Stopping of Sparse Search. A Strategic Negotiations Model with Applications to an International Crisis: Preliminary Report. Progressive Horizon Planning. Logical Modelling of Constraints on Acceptable Syntactic Tree Forms for Natural Language Analysis. A Statictical Filter for Resolving Pronoun References. "Form and Function": A Theory of Purposive, Qualitative 3-D Object Recognition. Dynamic Multiple-Motion Computation. Translating Default Theories to Logic Programs. An Efficient Algorithm for Point Selection for Image Surface Recovery Computation. The Generalized-Concepts Object-Centered World, and Possible Representations. Constructive Induction by Incremental Concept Formation.

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Research paper thumbnail of Near Field Photometric Stereo with Point Light Sources

SIAM Journal on Imaging Sciences, 2014

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Research paper thumbnail of Efficient Computation of Adaptive Threshold Surfaces for Image Binarization

The problem of binarization of gray level images acquired under nonuniform illumination is recons... more The problem of binarization of gray level images acquired under nonuniform illumination is reconsidered. Yanowitz and Bruckstein proposed to use for image binarization an adaptive threshold surface, determined by interpolation of the image gray levels at points where the image gradient is high. The rationale is that high image gradient indicates probable object edges, and there the image values are between the object and the background gray levels. The threshold surface was determined by successive overrelaxation as the solution of the Laplace equation. This work proposes a different method to determine an adaptive threshold surface. In this new method, inspired by multiresolution approximation, the threshold surface is constructed with considerably lower computational complexity and is smooth, yielding faster image binarizations and better visual performance.

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Research paper thumbnail of Pincer-based vs. Same-direction Search Strategies After Smart Evaders by Swarms of Agents

ArXiv, 2021

Suppose in a given planar region, there are smart mobile evaders and we want to detect them using... more Suppose in a given planar region, there are smart mobile evaders and we want to detect them using sweeping agents. We assume that the agents have line sensors of equal length. We propose procedures for designing cooperative sweeping processes that ensure successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a known limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity the sweeping agent must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present a quantitative and qualitative comparison a...

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Research paper thumbnail of Search for Smart Evaders with Swarms of Sweeping Agents

ArXiv, 2021

Suppose that in a given planar circular region, there are some smart mobile evaders and we would ... more Suppose that in a given planar circular region, there are some smart mobile evaders and we would like to find them using sweeping agents. We assume that each agent has a line sensor of length 2r. We propose procedures for designing cooperative sweeping processes that ensure the successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity that the sweeper swarm must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present results on the ...

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Research paper thumbnail of Holographic Sensing

ArXiv, 2018

Holographic representations of data encode information in packets of equal importance that enable... more Holographic representations of data encode information in packets of equal importance that enable progressive recovery. The quality of recovered data improves as more and more packets become available. This progressive recovery of the information is independent of the order in which packets become available. Such representations are ideally suited for distributed storage and for the transmission of data packets over networks with unpredictable delays and or erasures. Several methods for holographic representations of signals and images have been proposed over the years and multiple description information theory also deals with such representations. Surprisingly, however, these methods had not been considered in the classical framework of optimal least-squares estimation theory, until very recently. We develop a least-squares approach to the design of holographic representation for stochastic data vectors, relying on the framework widely used in modeling signals and images.

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Research paper thumbnail of Mathematical analysis / Theory of signals Best bases for signal spaces Bases optimales pour des espaces de signaux

Article history: Received 2 October 2016 Accepted 3 October 2016 Available online xxxx Presented ... more Article history: Received 2 October 2016 Accepted 3 October 2016 Available online xxxx Presented by Haïm Brézis We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix that summarizes the prior information we have on the signals we want to represent, achieving optimal progressive approximations. We also provide uniqueness proofs for the discrete cases. © 2016 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.

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Research paper thumbnail of On Stochastic Broadcast Control of Swarms

We present a model for controlling swarms of mobile agents via a broadcast control, detected by a... more We present a model for controlling swarms of mobile agents via a broadcast control, detected by a random number of agents in the swarm. The agents that detect the control signal become the ad-hoc leaders of the swarm, while they detect the exogenous control. The agents are assumed to be velocity controlled, identical, anonymous, oblivious units with unlimited visibility. Assuming unlimited visibility decouples the problem of emergent behavior in a swarm from that of keeping the visibility graph complete, which has been thoroughly discussed in [10]. Each agent applies a linear local gathering control, based on the relative position of its neighbors. The detected exogenous control is superimposed by the leaders on the local gathering control. We show that in each time interval of a piecewise constant system, where the system evolves as a time-independent dynamic linear system, the swarm asymptotically aligns on a line in the direction of the exogenous control and all the agents move w...

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Research paper thumbnail of A sharp relative isoperimetric inequality for the square

Comptes Rendus. Mathématique

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Research paper thumbnail of Holographic Image Sensing

Holographic representations of data enable distributed storage with progressive refinement when t... more Holographic representations of data enable distributed storage with progressive refinement when the stored packets of data are made available in any arbitrary order. In this paper, we propose and test patch-based transform coding holographic sensing of image data. Our proposal is optimized for progressive recovery under random order of retrieval of the stored data. The coding of the image patches relies on the design of distributed projections ensuring best image recovery, in terms of the ell_2\ell_2ell_2 norm, at each retrieval stage. The performance depends only on the number of data packets that has been retrieved thus far. Several possible options to enhance the quality of the recovery while changing the size and number of data packets are discussed and tested. This leads us to examine several interesting bit-allocation and rate-distortion trade offs, highlighted for a set of natural images with ensemble estimated statistical properties.

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Research paper thumbnail of E. Rivlin Department of Computer Science Israel Institute of Technology Technion Haifa, Israel

In this paper we discuss a new approach to invariant signatures for recognizing curves under view... more In this paper we discuss a new approach to invariant signatures for recognizing curves under viewing distortions and partial occlusion. The approach is intended to overcome the ill-posed problem of nding derivatives, on which local invariants usually depend. The basic idea is to use invariant nite di erences, with a scale parameter that determines the size of the di erencing interval. The scale parameter is allowed to vary so that we obtain a\ scale space"-like invariant representation of the curve, with larger di erence ...

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Research paper thumbnail of Two-Image Perspective Photometric Stereo Using Shape-from-Shading

Lecture Notes in Computer Science, 2013

ABSTRACT Shape-from-Shading and photometric stereo are two fundamental problems in Computer Visio... more ABSTRACT Shape-from-Shading and photometric stereo are two fundamental problems in Computer Vision aimed at reconstructing surface depth given either a single image taken under a known light source or multiple images taken under different illuminations, respectively. Whereas the former utilizes partial differential equation (PDE) techniques to solve the image irradiance equation, the latter can be expressed as a linear system of equations in surface derivatives when 3 or more images are given. It therefore seems that current photometric stereo techniques do not extract all possible depth information from each image by itself. This paper utilizes PDE techniques for the solution of the combined Shape-from-Shading and photometric stereo problem when only 2 images are available. Extending our previous results on this problem, we consider the more realistic perspective projection of surfaces during the photographic process. Under these assumptions, there is a unique weak (Lipschitz continuous) solution to the problem at hand, solving the well known convex/concave ambiguity of the Shape-from-Shading problem. We propose two approximation schemes for the numerical solution of this problem, an up-wind finite difference scheme and a Semi-Lagrangian scheme, and analyze their properties. We show that both schemes converge linearly and accurately reconstruct the original surfaces. In comparison with a similar method for the orthographic 2-image photometric stereo, the proposed perspective one outperforms the orthographic one. We also demonstrate the method on real-life images. Our results thus show that using methodologies common in the field of Shape-from-Shading it is possible to recover more depth information for the photometric stereo problem under the more realistic perspective projection assumption.

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Research paper thumbnail of Holographic Sensing

Holographic representations of data encode information in packets of equal importance that enable... more Holographic representations of data encode information in packets of equal importance that enable progressive recovery. The quality of recovered data improves as more and more packets become available. This progressive recovery of the information is independent of the order in which packets become available. Such representations are ideally suited for distributed storage and for the transmission of data packets over networks with unpredictable delays and or erasures. Several methods for holographic representations of signals and images have been proposed over the years and multiple description information theory also deals with such representations. Surprisingly, however, these methods had not been considered in the classical framework of optimal least-squares estimation theory, until very recently. We develop a least-squares approach to the design of holographic representation for stochastic data vectors, relying on the framework widely used in modeling signals and images.

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Research paper thumbnail of Pincer-based vs. Same-direction Search Strategies After Smart Evaders by Swarms of Agents

Suppose in a given planar region, there are smart mobile evaders and we want to detect them using... more Suppose in a given planar region, there are smart mobile evaders and we want to detect them using sweeping agents. We assume that the agents have line sensors of equal length. We propose procedures for designing cooperative sweeping processes that ensure successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a known limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity the sweeping agent must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present a quantitative and qualitative comparison a...

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Research paper thumbnail of Holographic Image Sensing

Holographic representations of data enable distributed storage with progressive refinement when t... more Holographic representations of data enable distributed storage with progressive refinement when the stored packets of data are made available in any arbitrary order. In this paper, we propose and test patch-based transform coding holographic sensing of image data. Our proposal is optimized for progressive recovery under random order of retrieval of the stored data. The coding of the image patches relies on the design of distributed projections ensuring best image recovery, in terms of the ℓ_2 norm, at each retrieval stage. The performance depends only on the number of data packets that has been retrieved thus far. Several possible options to enhance the quality of the recovery while changing the size and number of data packets are discussed and tested. This leads us to examine several interesting bit-allocation and rate-distortion trade offs, highlighted for a set of natural images with ensemble estimated statistical properties.

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Research paper thumbnail of Search for smart evaders with sweeping agents

Robotica, 2021

Suppose in a given planar circular region, there are smart mobile evaders and we want to find the... more Suppose in a given planar circular region, there are smart mobile evaders and we want to find them using sweeping agents. We assume the sweeping agents are in a line formation whose total length is predetermined. We propose procedures for designing a sweeping process that ensures the successful completion of the task, thereby deriving conditions on the sweeping velocity of the linear formation and its path. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. We present results on the search time given the initial conditions.

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Research paper thumbnail of Direct Shape Recovery from Photometric Stereo with Shadows

2013 International Conference on 3D Vision, 2013

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Research paper thumbnail of From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images

SIAM Review, 2009

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Research paper thumbnail of Optimized Overlay Metrology Marks: Theory and Experiment

IEEE Transactions on Semiconductor Manufacturing, 2004

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Research paper thumbnail of Design of shapes for precise image registration

IEEE Transactions on Information Theory, 1998

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Research paper thumbnail of Artificial intelligence and computer vision: proceedings of the seventh Israeli conference, 26-27 December, 1990, Ramat Gan, Israel

Structuring Events for their Pronominal Reference. Monitoring the Execution of Contextualised Exp... more Structuring Events for their Pronominal Reference. Monitoring the Execution of Contextualised Expianations. Exact Point Matching. Similarity-Invariant Recognition of Partially Occluded Planar Curves and Shapes. Robust Estimators in Computer Vision: An Introduction to Least Median of Squares Regression. On Optimal Stopping of Sparse Search. A Strategic Negotiations Model with Applications to an International Crisis: Preliminary Report. Progressive Horizon Planning. Logical Modelling of Constraints on Acceptable Syntactic Tree Forms for Natural Language Analysis. A Statictical Filter for Resolving Pronoun References. "Form and Function": A Theory of Purposive, Qualitative 3-D Object Recognition. Dynamic Multiple-Motion Computation. Translating Default Theories to Logic Programs. An Efficient Algorithm for Point Selection for Image Surface Recovery Computation. The Generalized-Concepts Object-Centered World, and Possible Representations. Constructive Induction by Incremental Concept Formation.

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Research paper thumbnail of Near Field Photometric Stereo with Point Light Sources

SIAM Journal on Imaging Sciences, 2014

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Research paper thumbnail of Efficient Computation of Adaptive Threshold Surfaces for Image Binarization

The problem of binarization of gray level images acquired under nonuniform illumination is recons... more The problem of binarization of gray level images acquired under nonuniform illumination is reconsidered. Yanowitz and Bruckstein proposed to use for image binarization an adaptive threshold surface, determined by interpolation of the image gray levels at points where the image gradient is high. The rationale is that high image gradient indicates probable object edges, and there the image values are between the object and the background gray levels. The threshold surface was determined by successive overrelaxation as the solution of the Laplace equation. This work proposes a different method to determine an adaptive threshold surface. In this new method, inspired by multiresolution approximation, the threshold surface is constructed with considerably lower computational complexity and is smooth, yielding faster image binarizations and better visual performance.

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Research paper thumbnail of Pincer-based vs. Same-direction Search Strategies After Smart Evaders by Swarms of Agents

ArXiv, 2021

Suppose in a given planar region, there are smart mobile evaders and we want to detect them using... more Suppose in a given planar region, there are smart mobile evaders and we want to detect them using sweeping agents. We assume that the agents have line sensors of equal length. We propose procedures for designing cooperative sweeping processes that ensure successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a known limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity the sweeping agent must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present a quantitative and qualitative comparison a...

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Research paper thumbnail of Search for Smart Evaders with Swarms of Sweeping Agents

ArXiv, 2021

Suppose that in a given planar circular region, there are some smart mobile evaders and we would ... more Suppose that in a given planar circular region, there are some smart mobile evaders and we would like to find them using sweeping agents. We assume that each agent has a line sensor of length 2r. We propose procedures for designing cooperative sweeping processes that ensure the successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity that the sweeper swarm must have. This critical velocity is derived to ensure the satisfaction of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present results on the ...

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Research paper thumbnail of Holographic Sensing

ArXiv, 2018

Holographic representations of data encode information in packets of equal importance that enable... more Holographic representations of data encode information in packets of equal importance that enable progressive recovery. The quality of recovered data improves as more and more packets become available. This progressive recovery of the information is independent of the order in which packets become available. Such representations are ideally suited for distributed storage and for the transmission of data packets over networks with unpredictable delays and or erasures. Several methods for holographic representations of signals and images have been proposed over the years and multiple description information theory also deals with such representations. Surprisingly, however, these methods had not been considered in the classical framework of optimal least-squares estimation theory, until very recently. We develop a least-squares approach to the design of holographic representation for stochastic data vectors, relying on the framework widely used in modeling signals and images.

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Research paper thumbnail of Mathematical analysis / Theory of signals Best bases for signal spaces Bases optimales pour des espaces de signaux

Article history: Received 2 October 2016 Accepted 3 October 2016 Available online xxxx Presented ... more Article history: Received 2 October 2016 Accepted 3 October 2016 Available online xxxx Presented by Haïm Brézis We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix that summarizes the prior information we have on the signals we want to represent, achieving optimal progressive approximations. We also provide uniqueness proofs for the discrete cases. © 2016 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.

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Research paper thumbnail of On Stochastic Broadcast Control of Swarms

We present a model for controlling swarms of mobile agents via a broadcast control, detected by a... more We present a model for controlling swarms of mobile agents via a broadcast control, detected by a random number of agents in the swarm. The agents that detect the control signal become the ad-hoc leaders of the swarm, while they detect the exogenous control. The agents are assumed to be velocity controlled, identical, anonymous, oblivious units with unlimited visibility. Assuming unlimited visibility decouples the problem of emergent behavior in a swarm from that of keeping the visibility graph complete, which has been thoroughly discussed in [10]. Each agent applies a linear local gathering control, based on the relative position of its neighbors. The detected exogenous control is superimposed by the leaders on the local gathering control. We show that in each time interval of a piecewise constant system, where the system evolves as a time-independent dynamic linear system, the swarm asymptotically aligns on a line in the direction of the exogenous control and all the agents move w...

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Research paper thumbnail of A sharp relative isoperimetric inequality for the square

Comptes Rendus. Mathématique

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Research paper thumbnail of Holographic Image Sensing

Holographic representations of data enable distributed storage with progressive refinement when t... more Holographic representations of data enable distributed storage with progressive refinement when the stored packets of data are made available in any arbitrary order. In this paper, we propose and test patch-based transform coding holographic sensing of image data. Our proposal is optimized for progressive recovery under random order of retrieval of the stored data. The coding of the image patches relies on the design of distributed projections ensuring best image recovery, in terms of the ell_2\ell_2ell_2 norm, at each retrieval stage. The performance depends only on the number of data packets that has been retrieved thus far. Several possible options to enhance the quality of the recovery while changing the size and number of data packets are discussed and tested. This leads us to examine several interesting bit-allocation and rate-distortion trade offs, highlighted for a set of natural images with ensemble estimated statistical properties.

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