Sparsity and `Something Else': An Approach to Encrypted Image Folding

A property of sparse representations in relation to their capacity for information storage is discussed. It is shown that this feature can be used for an application that we term Encrypted Image Folding. The proposed procedure is realizable through any suitable transformation. In particular, in this paper we illustrate the approach by recourse to the Discrete Cosine Transform and a combination of redundant Cosine and Dirac dictionaries. The main advantage of the proposed technique is that both storage and encryption can be achieved simultaneously using simple processing steps.Comment: Revised manuscript- Software for implementing the Encrypted Image Folding proposed in this paper is available on http://www.nonlinear-approx.info

Sparse Representation of Astronomical Images

Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm: i)Effectiveness at producing sparse representations. ii)Competitiveness, with respect to the time required to process large images.The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks.This feature makes it possible to apply the effective greedy selection technique Orthogonal Matching Pursuit, up to some block size. For blocks exceeding that size a refinement of the original Matching Pursuit approach is considered. The resulting method is termed Self Projected Matching Pursuit, because is shown to be effective for implementing, via Matching Pursuit itself, the optional back-projection intermediate steps in that approach.Comment: Software to implement the approach is available on http://www.nonlinear-approx.info/examples/node1.htm

Sparse Spike Coding : applications of Neuroscience to the processing of natural images

If modern computers are sometimes superior to humans in some specialized tasks such as playing chess or browsing a large database, they can't beat the efficiency of biological vision for such simple tasks as recognizing and following an object in a complex cluttered background. We present in this paper our attempt at outlining the dynamical, parallel and event-based representation for vision in the architecture of the central nervous system. We will illustrate this on static natural images by showing that in a signal matching framework, a L/LN (linear/non-linear) cascade may efficiently transform a sensory signal into a neural spiking signal and we will apply this framework to a model retina. However, this code gets redundant when using an over-complete basis as is necessary for modeling the primary visual cortex: we therefore optimize the efficiency cost by increasing the sparseness of the code. This is implemented by propagating and canceling redundant information using lateral interactions. We compare the efficiency of this representation in terms of compression as the reconstruction quality as a function of the coding length. This will correspond to a modification of the Matching Pursuit algorithm where the ArgMax function is optimized for competition, or Competition Optimized Matching Pursuit (COMP). We will in particular focus on bridging neuroscience and image processing and on the advantages of such an interdisciplinary approach.Comment: http://incm.cnrs-mrs.fr/LaurentPerrinet/Publications/Perrinet08spi

Clutter Mitigation in Echocardiography Using Sparse Signal Separation

In ultrasound imaging, clutter artifacts degrade images and may cause inaccurate diagnosis. In this paper, we apply a method called Morphological Component Analysis (MCA) for sparse signal separation with the objective of reducing such clutter artifacts. The MCA approach assumes that the two signals in the additive mix have each a sparse representation under some dictionary of atoms (a matrix), and separation is achieved by finding these sparse representations. In our work, an adaptive approach is used for learning the dictionary from the echo data. MCA is compared to Singular Value Filtering (SVF), a Principal Component Analysis- (PCA-) based filtering technique, and to a high-pass Finite Impulse Response (FIR) filter. Each filter is applied to a simulated hypoechoic lesion sequence, as well as experimental cardiac ultrasound data. MCA is demonstrated in both cases to outperform the FIR filter and obtain results comparable to the SVF method in terms of contrast-to-noise ratio (CNR). Furthermore, MCA shows a lower impact on tissue sections while removing the clutter artifacts. In experimental heart data, MCA obtains in our experiments clutter mitigation with an average CNR improvement of 1.33 dB