Test Problems Sample Clauses

Test Problems. To illustrate the behavior of our proposed methods, we use six test problems. The first problem comes from the iterative image deblurring package, ‘Re- storeTools’ [96]. Image deblurring has the form (1.1), where the vector x true represents the true image scene, A is a matrix representing a blurring oper- ation, and b is a vector representing the observed, blurred and noisy image. Given the blurred image and information regarding the blur, the aim is to reconstruct an approximation of the true image. The RestoreTools package has several data sets and tools (such as matrix construction and multiplica- tion routines) that can be used with iterative methods. The data set we use consists of a true image of a Satellite and a so-called point spread function (PSF) that defines the blurring operation. The matrix A is constructed from the PSF, using a matrix construction routine in RestoreTools. We then form the noise-free blurred image as b true = Ax true. The Matlab instructions are the following: >> load satellite >> A = psfMatrix(PSF); >> b_true = A*x_true; The images have 256 × 256 pixels, so the vectors b true and x true have length 2562 = 65, 536. The function psfMatrix uses an efficient data structure scheme to represent the 65, 536 × 65, 536 matrix A, and the multiplication operator, *, is overloaded to allow for efficient computation of matrix-vector multiplications. For more details, see [96]. The other five test problems are taken from the ‘Regularization Tools’ pack- age [67]. In each case we generate an n × n matrix A, true solution vector x true, and (noise-free) observation vector b true, setting n = 256. • Xxxxxxxx is Xxxxxxxx’ “famous” test problem. A, b, and x true are ob- tained by discretizing the first kind Fredholm integral equation b(s) = ∫
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