IEEE Trans Image Process - Gradient-based image recovery methods from incomplete Fourier measurements.

Tópicos

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Resumo

A major problem in imaging applications such as magnetic resonance imaging and synthetic aperture radar is the task of trying to reconstruct an image with the smallest possible set of Fourier samples, every single one of which has a potential time and/or power cost. The theory of compressive sensing (CS) points to ways of exploiting inherent sparsity in such images in order to achieve accurate recovery using sub-Nyquist sampling schemes. Traditional CS approaches to this problem consist of solving total-variation (TV) minimization programs with Fourier measurement constraints or other variations thereof. This paper takes a different approach. Since the horizontal and vertical differences of a medical image are each more sparse or compressible than the corresponding TV image, CS methods will be more successful in recovering these differences individually. We develop an algorithm called GradientRec that uses a CS algorithm to recover the horizontal and vertical gradients and then estimates the original image from these gradients. We present two methods of solving the latter inverse problem, i.e., one based on least-square optimization and the other based on a generalized Poisson solver. After a thorough derivation of our complete algorithm, we present the results of various experiments that compare the effectiveness of the proposed method against other leading methods.

Resumo Limpo

major problem imag applic magnet reson imag synthet apertur radar task tri reconstruct imag smallest possibl set fourier sampl everi singl one potenti time andor power cost theori compress sens cs point way exploit inher sparsiti imag order achiev accur recoveri use subnyquist sampl scheme tradit cs approach problem consist solv totalvari tv minim program fourier measur constraint variat thereof paper take differ approach sinc horizont vertic differ medic imag spars compress correspond tv imag cs method will success recov differ individu develop algorithm call gradientrec use cs algorithm recov horizont vertic gradient estim origin imag gradient present two method solv latter invers problem ie one base leastsquar optim base general poisson solver thorough deriv complet algorithm present result various experi compar effect propos method lead method

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