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Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with ‘typical’/‘random’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP),(More)
We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal number of pixels, and yet be accurately reconstructed. The(More)
The minimum `1-norm solution to an underdetermined system of linear equations y = Ax, is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest in signal processing and information transmission. However, general-purpose optimizers are much too slow for `1 minimization in many large-scale applications. The(More)
Finding the sparsest solution to underdetermined systems of linear equations <i>y</i> = &#x03A6;<sub>x</sub> is NP-hard in general. We show here that for systems with &#x201C;typical&#x201D;/&#x201C;random&#x201D; &#x03A6;, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our(More)
The minimum `1-norm solution to an underdetermined system of linear equations y = Ax, is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest in signal processing and information transmission. However, general-purpose optimizers are much too slow for `1 minimization in many large-scale applications. The(More)
The emerging video coding standard MPEG-4 enables various content-based functionalities for multimedia applications. To support such functionalities, as well as to improve coding efficiency, MPEG-4 relies on a decomposition of each frame of an image sequence into video object planes (VOPs). Each VOP corresponds to a single moving object in the scene. This(More)
Recent work on block-based compression for low bit-rate coding has shown that employing a block coder within a sampling scheme where the image is downsampled prior to coding (and upsampled after the decoding stage) results in superior performance compared to standard block coding. In this paper, we explore the use of optimal decimation and interpolation(More)
Block coders are among the most common compression tools available for still images and video sequences. Their low computational complexity along with their good performance make them a popular choice for compression of natural images. Yet, at low bitrates, block coders introduce visually annoying artifacts into the image. One approach that alleviates this(More)
The emerging video coding standard MPEG-4 enables various content-based functionalities for multimedia applications. To support such functionalities, as well as to improve coding efficiency, MPEG-4 relies on a decomposition of each frame of an image sequence into video object planes (VOP’s). Each VOP corresponds to a single moving object in the scene. In(More)
We present a fast and accurate Discrete Spiral Fourier Transform and its inverse. The inverse solves the problem of reconstructing an image from MRI data acquired along a spiral k-space trajectory. First, we define the spiral FT and its adjoint. These discrete operators allow us to efficiently compute the inverse using fast-converging conjugate gradient(More)