### Adaptive compressed sensing – a new class of self-organizing coding models

"... for neuroscience ..."

(Show Context)
### doi:10.1155/2008/513706 Research Article Adaptive Reference Levels in a Level-Crossing Analog-to-Digital Converter

"... Level-crossing analog-to-digital converters (LC ADCs) have been considered in the literature and have been shown to efficiently sample certain classes of signals. One important aspect of their implementation is the placement of reference levels in the converter. The levels need to be appropriately l ..."

Abstract
- Add to MetaCart

(Show Context)
Level-crossing analog-to-digital converters (LC ADCs) have been considered in the literature and have been shown to efficiently sample certain classes of signals. One important aspect of their implementation is the placement of reference levels in the converter. The levels need to be appropriately located within the input dynamic range, in order to obtain samples efficiently. In this paper, we study optimization of the performance of such an LC ADC by providing several sequential algorithms that adaptively update the ADC reference levels. The accompanying performance analysis and simulation results show that as the signal length grows, the performance of the sequential algorithms asymptotically approaches that of the best choice that could only have been chosen in hindsight within a family of possible schemes. Copyright © 2008 Karen M. Guan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.

### Complex Illumination Relighting Natural Illumination Relighting Reference Photograph

, 2008

"... Figure 1: An example of relit images of a scene generated from a reflectance field captured using just 1000 non-adaptive illumination patterns (emitted from the right onto the scene). The incident lighting resolution, and resolution of each reflectance function, is 128 × 128. Even though we only per ..."

Abstract
- Add to MetaCart

Figure 1: An example of relit images of a scene generated from a reflectance field captured using just 1000 non-adaptive illumination patterns (emitted from the right onto the scene). The incident lighting resolution, and resolution of each reflectance function, is 128 × 128. Even though we only performed a small number of measurements, we are still able to capture and represent complex light transport paths. Left: the scene relit with a high frequency illumination condition (inset). Middle: the scene relit under a natural illumination condition (inset). Right: a ground truth reference photograph of the scene. In this paper we propose a new framework for capturing light transport data of a real scene, based on the recently developed theory of compressive sensing. Compressive sensing offers a solid mathematical framework to infer a sparse signal from a limited number of non-adaptive measurements. Besides introducing compressive sensing for fast acquisition of light transport to computer graphics, we develop several innovations that address specific challenges for image-based relighting, and which may have broader implications. We develop a novel hierarchical decoding algorithm that improves reconstruction quality by exploiting inter-pixel coherency relations. Additionally, we design new non-adaptive illumination patterns that minimize measurement noise and further improve reconstruction quality. We illustrate our framework by capturing detailed highresolution reflectance fields for image-based relighting. 1

### Secure Data Transmission Scheme Based on Compressive Sensing Theory ⋆

"... In compressive sensing, a signal can be reconstructed from a small set of non-adaptive, linear measurements if the signal can be represented as a sparse objective in some orthonormal basis. We propose a compressive sensing based secure data transmission scheme in this paper. Only simple linear opera ..."

Abstract
- Add to MetaCart

(Show Context)
In compressive sensing, a signal can be reconstructed from a small set of non-adaptive, linear measurements if the signal can be represented as a sparse objective in some orthonormal basis. We propose a compressive sensing based secure data transmission scheme in this paper. Only simple linear operations are required in the encryption end and complex computations are transferred to the resource-rich decryption end. The encryption phase and decryption phase are described in detail. We also provide the perfect secrecy proof and the experiment results of signal and image encryption to verify the effectiveness of the proposed scheme.

### Adobe Inc.

"... In this article we propose a new framework for capturing light transport data of a real scene, based on the recently developed theory of compressive sensing. Compressive sensing offers a solid mathematical framework to infer a sparse signal from a limited number of nonadaptive measurements. Besides ..."

Abstract
- Add to MetaCart

In this article we propose a new framework for capturing light transport data of a real scene, based on the recently developed theory of compressive sensing. Compressive sensing offers a solid mathematical framework to infer a sparse signal from a limited number of nonadaptive measurements. Besides introducing compressive sensing for fast acquisition of light transport to computer graphics, we develop several innovations that address specific challenges for imagebased relighting, and which may have broader implications. We develop a novel hierarchical decoding algorithm that improves reconstruction quality by exploiting interpixel coherency relations. Additionally, we design new nonadaptive illumination patterns that minimize measurement noise and further improve reconstruction quality. We illustrate our framework by capturing detailed high-resolution reflectance fields for image-based relighting.

### Mention: « STIC (Science et technologies de l’information et de la communication) »

"... l-0 ..."

(Show Context)
### Abstract

, 906

"... Adaptive compressed sensing – a new class of self-organizing coding models for neuroscience ..."

Abstract
- Add to MetaCart

(Show Context)
Adaptive compressed sensing – a new class of self-organizing coding models for neuroscience

### • Sparse Linear Model: y = Xu + ε

"... • Compressed Sensing (CS) = exploit signal compressibility to improve signal acquisition • Example: Digital camera with DCT (JPEG), do not measure every single pixel •CS Recipe: Sample random projections, apply a reconstruction algorithm to get the signal [1, 2]. • Valid if signal is unstructured e ..."

Abstract
- Add to MetaCart

(Show Context)
• Compressed Sensing (CS) = exploit signal compressibility to improve signal acquisition • Example: Digital camera with DCT (JPEG), do not measure every single pixel •CS Recipe: Sample random projections, apply a reconstruction algorithm to get the signal [1, 2]. • Valid if signal is unstructured except for sparsity • Images have a lot of additional structure [4, 5] • Are random measurements optimal for images? • In this study we compare: – Wavelet measurements top down – Random measurements (suggested by CS) – Actively designed measurements based on an efficient Bayesian approach

### 1 Informative Sensing

, 2009

"... Compressed sensing is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random measurements allow perfect reconstruction while measurements based ..."

Abstract
- Add to MetaCart

(Show Context)
Compressed sensing is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random measurements allow perfect reconstruction while measurements based on principal component analysis (PCA) or independent component analysis (ICA) do not. At the same time, for other signal and noise distributions, PCA and ICA can significantly outperform random projections in terms of enabling reconstruction from a small number of measurements. In this paper we ask: given the distribution of signals we wish to measure, what are the optimal set of linear projections for compressed sensing? We consider the problem of finding a small number of linear projections that are maximally informative about the signal. Formally, we use the InfoMax criterion and seek to maximize the mutual information between the signal, x, and the (possibly noisy) projection y = Wx. We show that in general the optimal projections are not the principal components of the data nor random projections, but rather a seemingly novel set of projections that capture what is still uncertain about the signal, given the knowledge of distribution. We present analytic solutions for certain special cases including natural images. In particular, for natural images, the near-optimal projections are bandwise random, i.e., incoherent to the sparse bases at a particular frequency band but with more weights on the low-frequencies, which has a physical relation to the multi-resolution representation of images. Index Terms sensing.

### Sequential Compressed Sensing 1

"... Abstract—Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable performance by bounding the number of samples requ ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract—Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable performance by bounding the number of samples required for a given level of signal sparsity. However, using these bounds to minimize the number of samples requires a-priori knowledge of the sparsity of the unknown signal, or the decay structure for near-sparse signals. Furthermore, there are some popular recovery methods for which no such bounds are known. In this paper, we investigate an alternative scenario where observations are available in sequence. For any recovery method, this means that there is now a sequence of candidate reconstructions. We propose a method to estimate the reconstruction error directly from the samples themselves, for every candidate in this sequence. This estimate is universal in the sense that it is based only on the measurement ensemble, and not on the recovery method or any assumed level of sparsity of the unknown signal. With these estimates, one can now stop observations as soon as there is reasonable certainty of either exact or sufficiently accurate reconstruction. They also provide a way to obtain “run-time ” guarantees for recovery methods that otherwise lack a-priori performance bounds. We investigate both continuous (e.g. Gaussian) and discrete (e.g. Bernoulli or Fourier) random measurement ensembles, both for exactly sparse and general near-sparse signals, and with both noisy and noiseless measurements. Index Terms—Compressed sensing, sequential measurements, optimal stopping rule. I.