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The proposed approach exploits the structure of both the down-sampling and the blur operators in the frequency domain and computes the optimal regularisation parameter as the one optimising a suitably defined residual whiteness measure. Computationally, the proposed strategy relies on the fast solution of generalised Tikhonov <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ell _2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>\u2013<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ell _2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> problems as proposed in Zhao et al. (IEEE Trans Image Process 25:3683\u20133697, 2016). These problems naturally appear as substeps of the Alternating Direction Method of Multipliers used to solve single image super-resolution problems with non-quadratic, non-smooth, sparsity-promoting regularisers both in convex and in non-convex regimes. After detailing the theoretical properties allowing to express the whiteness functional in a compact way, we report an exhaustive list of numerical experiments proving the effectiveness of the proposed approach for different type of problems, in comparison with well-known parameter selection strategies such as, e.g., the discrepancy principle.<\/jats:p>","DOI":"10.1007\/s10851-022-01110-1","type":"journal-article","created":{"date-parts":[[2022,7,5]],"date-time":"2022-07-05T13:13:42Z","timestamp":1657026822000},"page":"99-123","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["ADMM-Based Residual Whiteness Principle for Automatic Parameter Selection in Single Image Super-Resolution Problems"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3074-1550","authenticated-orcid":false,"given":"Monica","family":"Pragliola","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luca","family":"Calatroni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Lanza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fiorella","family":"Sgallari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,5]]},"reference":[{"key":"1110_CR1","doi-asserted-by":"publisher","first-page":"2751","DOI":"10.1109\/TIP.2013.2257810","volume":"22","author":"MSC Almeida","year":"2013","unstructured":"Almeida, M.S.C., Figueiredo, M.A.T.: Parameter estimation for blind and non-blind deblurring using residual whiteness measures. 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